1 Find dy/dx if y = 4x ^3 - 3 x^ 2 + 2x
2 Differentiate with respect to x
y = 5 x ^3 - 2 x^ -2 + 1
(3) Find dy/dx at x = ñ/8 if y = 6 x^ 2 + 2 sin x
(4) Differentiate , with respect to ø if
v = 2ø ^ 3 + 2 cos ø + sin ø
(5) Integratewith respect to x
2 x^ 4 + 4/x^ 2+ x
6. Integrate w.r.t. x
2 x ^2( 2x + 3 ) Hint Expand then integrate
7 Integrate (1 + 2 sin x ) wrt x with 45 and 0 degrees as bounds
8. Integrate 2x + 3 cos x ) wrt x with 90 and 60 degrees as bounds
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1) y = 4x^3 - 3x^2 + 2x
ReplyDeletedy/dx = 3(4)(x^3-1) - 2(3)(x^2-1) + 1(1)(x^1-1)
= 12x^2 - 6x + 2
2) y = 5x^3 - 2x^-2 + 1
ReplyDeletedy/dx = 3(5)(x^3-1) - (-2)(2)(x^-2-1) + 0(1)(x^0)
= 15x^2 + 4x^-3
3) y = 6x^2 + 2sinx
ReplyDeletedy/dx = 2(6)(x^2-1) + 1(2)(cos)(x)
= 12x + 2cosx
x = ñ/8
therefore:
dy/dx = 12(ñ/8) + 2cos(ñ/8)
= 3ñ/2 + cosñ/4
4) v = 2ø^3 + 2cosø + sinø
ReplyDeletedv/dø = 3(2)(ø^3-1) - 1 (2)(sin)(ø) + 1(cos)(ø)
= 6ø^2 - 2sinø + cosø
num(5)
ReplyDelete2x^4+4/x^2+x
2x^4+4x^-2+x
2x^5/5+4x^-1/-1+x^1/1 +c
correct me if i am incorrect
num (6)
ReplyDelete2x^2(2x+3)
4x^3+6x^2
4x^4/4+6x^3/3
x^4+2x^3 +C
num(7)
ReplyDelete1+2sinx
x-2cosx
bounds between 45 and 0
ithink you have to put your calculator on radians mode
(45-2cos(45))-(0-2cos(0))
(43.95)-(-2)=45.95
i dont know if this correct
y = 4x ^3 - 3 x^ 2 + 2x
ReplyDeleteUsing anx^n-1: dy/dx 4(3)x^3-1-3(2)x^2-1+2(1)x^1-1.
dy/dx 12x^2-6x+2.
y = 5 x ^3 - 2 x^ -2 + 1.
ReplyDeletedy/dx = 15x^2+4x^-3.
4x^3-3x^2+2x
ReplyDeletedy/dx=4(3)(x^3-1)-3(2)(x^2-1)+2
=12x^2-6x
in question 1: y = 4x^3 - 3x^2 + 2x
ReplyDeletethe deferential of 4x^3 = 3(4)x^(3-1)
= 12x^2
the deferential of 3x^2 = 2(3)x^(2-1)
= 6x
the deferential of 2x = 2
hence:
dy/dx = 12x^2 - 6x + 2
in question 2: y = 5x^3 - 2x^-2 + 1
ReplyDeletewith respect to x:
the deferential of 5x^3 = 3(5)x^(3-1)
= 15x^2
the deferential of 2x^-2 = -2(2)x^(-2-1)
= -4x^-3
the deferential of 1 = 0
hence:
dy/dx = 15x^2 + 4x^-3
4)
ReplyDeletev=2@^2+2cos@+sin@
then dv/d@ = 3(2)@^2-2sin@+cos@
= 6@^2-2sin@+cos@
1 y = 4x ^3 - 3 x^ 2 + 2x
ReplyDeletedy/dx = 12x^2 - 6x + 2
2 y = 5 x ^3 - 2 x^ -2 + 1
ReplyDeletedy/dx = 15x^2 +4x^-3
(4)v = 2ø ^ 3 + 2 cos ø + sin ø
ReplyDeletedv/dø = 6ø^2 - 2sin ø + cos ø
2 x^ 4 + 4/x^ 2+ x
ReplyDeletedy/dx = 8x^3 - 8x^-3 + 1
1. y = 4x^3 - 3x^2 + 2x
ReplyDeletedy/dx = 3(4)[x^(3-1)] - 2(3)[x^(2-1)] + 2[x^(1-1)]
= 12x^2 - 6x + 2
2) y = 5x^3 - 2x^-2 + 1
ReplyDeletedy/dx = 3(5)[x^(3-1)] - (-2)(2)[x^(-2-1)] + 0
= 15x^2 + 4x^-3
3. y = 6 x^ 2 + 2 sin x
ReplyDeletedy/dx = 12 x + 2 cosx
when x = ñ/8
dy/dx = 12(ñ/8) + 2cos(ñ/8)
= 3/2ñ + 1.85
= 4.71 + 1.85
= 6.56
4. v = 2ø ^ 3 + 2 cos ø + sin ø
ReplyDeletedv/dø= 2(3)[ø^(3-1)] +2 (-sinø) + cosø
= 6ø^2 - 2sinø + cosø
5. 2 x^ 4 + 4/x^ 2+ x
ReplyDeletebring downstairs up:
2x^4 + 4x^-2 + x
integrate:
[2/(4+1)] x^(4+1) + [4/(-2+1)]x^(-2+1) + [1/(1+1)] x^(1+1)
2/5 x^5 - 4x^-1 + x^2/2
when y =4x^3-3x^2+2x
ReplyDeletedy/dx= 3(4)(x^3-1)-2(3)(x^2-1)+1(1)(x^1-1)
=12x^2-6x+2
1)
ReplyDeletey=4x^3-3x^2+2x
dy/dx= 12x^2-6x+2
2)
ReplyDeletedy/dx=5x^3-2x^-2+1
=15x^2+4x^-3
5)
ReplyDeletey=2x^4+4/x^2+x dx
y=2x^4+4x^-2+x dx
y=2x^5/5+4x^-1+x^2/2
6)
ReplyDeletey=2x^2(2x+3)
y=4x^3+6x^2 dx
y=4x^4/4+6x^3/3
1. dy/dx=12x^2-6x+2
ReplyDeletedy/dx= 15x^2 + 4X^-3
ReplyDeletey=4x^3-3x^2+ 2x
ReplyDeletedy/dx=3(4)(x^3-1)- 2(3)(x^2-1) + 1(1)(x^1-1)
= 12x^2 - 6x + 2
2. y = 5x^3 - 2x^-2 + 1
ReplyDeletedy/dx = 3(5)(x^3-1) - (-2)(2)(x^-2-1) + 0(1)(x^0)
= 15x^2 + 4x^-3
5. 2 x^ 4 + 4/x^ 2+ x
ReplyDelete2x^4 + 4x^-2 + x
[2/(4+1)] x^(4+1) + [4/(-2+1)]x^(-2+1) + [1/(1+1)] x^(1+1)
2/5 x^5 - 4x^-1 + x^2/2
7.(1 + 2 sin x )
ReplyDeletex-2cosx
sub 45 degrees an 0
(45-2cos(45))
(43.95)
i not sure if this correct if not then what is teh correct answer
(1)
ReplyDeletey = 4x ^3 - 3 x^ 2 + 2x
dy/dx= (4*3)x^(3-1) - (3*2)x^(2-1) + 2 x^(1-1)
dy/dx= 12x^2 - 6x + 2
2 Differentiate with respect to x
ReplyDelete(2) y = 5 x ^3 - 2 x^ -2 + 1
dy/dx= (5*3)x^(3-1) - (2*-2)x^(-2-1)
dy/dx= 15x^2 + 4x^-3
dy/dx= 15x^2 + 4/x^3
(3) Find dy/dx at x = ñ/8 if y = 6 x^ 2 + 2 sin x
ReplyDeletey = 6 x^ 2 + 2 sin x
dy/dx= (6*2)x^(2-1) + 2 cosx
dy/dx= 12x + 2 cosx
sub x= ñ/8
dy/dx= 12(ñ/8) + 2 cos(ñ/8)
dy/dx= 12ñ/8 + 2 cos ñ/8
dy/dx= 3ñ/ 2 + 2 cos ñ/8
divide the equation by 2
therefore : dy/dx= 3ñ + 2cos ñ/4
(4)
ReplyDeletev = 2ø ^ 3 + 2 cos ø + sin ø
dv/dø= (2*3)ø^ (3-1) - 2 sin ø + cos ø
dv/dø= 6ø^2 - 2 sin ø + cos ø
(5) Integratewith respect to x
ReplyDelete2 x^ 4 + 4/x^ 2+ x
(5)2 x^ 4 + 4/x^ 2+ x
∫2x^4 + 4x^-2 + x dx
= ∫(2x^(4+1))/(4+1)+ (4x^ (-2+1))/ (-2+1) + (x^(1+1))/(1+1)
= ∫ ((2x^5)/5) + (4x^-1)/-1) + ((x^2)/2)
6. Integrate w.r.t. x
ReplyDelete2 x ^2( 2x + 3 ) Hint Expand then integrate
2 x ^2( 2x + 3 )
=2x^2 * 2x + 2x^2 *3
= 4x^3 + 6x^2
= ∫ 4x^3 + 6x^2
= ∫ (4x^(3+1))/(3+1)) + (6x^(2+1)/(2+1))
=∫ (4x^4)/4 + (6x^3)/3
=∫ x^4 + 2x^3
number1
ReplyDeletey = 4x ^3 - 3 x^ 2 + 2x
dy/dx= 12x^2- 6x+ 2
number2
ReplyDeleteshowing full steps (sorry about the above one)
y = 5 x ^3 - 2 x^-2 + 1
dy/dx= (3)5x^(3-1)- (1)2x^(-2-1)
= 15x^2 - 2x^-3
1.
ReplyDeletey = 4x^3 - 3x^2 + 2x
dy/dx = 12x^2 - 6x + 2
2.
ReplyDeletey = 5x^3 - 2x^-2 + 1
dy/dx = 15x^2 +4x^-3
4.
ReplyDeletev = 2ø^3 + 2cosø + sinø
dv/dø = 6ø^2 - 2sinø + cosø
5.
ReplyDeletey=2x^4+4/x^2+x dx
y=2x^4+4x^-2+x dx
integral=2x^5/5+4x^-1+x^2/2
1).
ReplyDeletey= 4x^3-3X^2+2X
dy/dx= 12x^2-6x+2
2).
ReplyDeletey= 5x^3-2x^-2+1
dy/dx= 15x^2+4x^-3
3).
ReplyDeletey= 6x^2+2 sin x
dy/dx= 12x+2 cos x
when x= n/8
dy/dx= 12(n/8)+2 cos(n/8)
4).
ReplyDeletev=2@^3+2cos@+cos@
dv/d@=6@^2-2sin@+cos@
5).
ReplyDelete2x^4+4/x^2+x
the integral of that is 8x^5/5-8x^-1/-1+x^2/2+c
= 8x^5/5+8x^-1+x^2/2+c
6).
ReplyDelete2x^2(2x+3)
4x^3+6x^2
the integral of that is 4x^4/4+6x^3/3
= x^4+2x^3
7).
ReplyDelete1+2sinx
the integral of that is x-2cosx
using the bounds 45 and 0 degrees
[45-2cos45]-[0-2cos0]
43.59-2
41.59
8).
ReplyDelete2x+3cosx
the integral of that is 2x^2/2+3sinx
= x^2+3sinx
using bounds 90 and 60 degrees.
[(90)^2+3sin90]-[(60)^2+3sin60]
8103-3602.60
4500.4
(3) Find dy/dx at x = ñ/8 if y = 6 x^ 2 + 2 sin x
ReplyDeletey = 6 x^ 2 + 2 sin x
dy/dx= (6*2)x^(2-1) + 2 cosx
dy/dx= 12x + 2 cosx
sub x= ñ/8
dy/dx= 12(ñ/8) + 2 cos(ñ/8)
dy/dx= 12ñ/8 + 2 cos ñ/8
dv/dø = 6ø^2 - 2sin ø + cos ø
ReplyDeletefor question 1
ReplyDeletey = 4x^3 - 3x^2 + 2x
dy/dx = 3(4)(x^3-1) - 2(3)(x^2-1) + 1(1)(x^1-1)
= 12x^2 - 6x + 2
question 6
ReplyDelete2x^2(2x+3)
4x^3+6x^2
4x^4/4+6x^3/3
x^4+2x^3 +C
correct?
can sum1 please tell me what w.r.t means
ReplyDelete1. y = 4x^3 - 3x^2 + 2x
ReplyDeletedy/dx = 3(4)[x^(3-1)] - 2(3)[x^(2-1)] + 2[x^(1-1)]
= 12x^2 - 6x + 2
2) y = 5x^3 - 2x^-2 + 1
ReplyDeletedy/dx = 3(5)[x^(3-1)] - (-2)(2)[x^(-2-1)] + 0
= 15x^2 + 4x^-3
3. y = 6 x^ 2 + 2 sin x
ReplyDeletedy/dx = 12 x + 2 cosx
when x = ñ/8
dy/dx = 12(ñ/8) + 2cos(ñ/8)
= 3/2ñ + 1.85
= 4.71 + 1.85
= 6.56
4. v = 2ø ^ 3 + 2 cos ø + sin ø
ReplyDeletedv/dø= 2(3)[ø^(3-1)] +2 (-sinø) + cosø
= 6ø^2 - 2sinø + cosø
5. 2 x^ 4 + 4/x^ 2+ x
ReplyDeletebring downstairs up:
2x^4 + 4x^-2 + x
integrate:
[2/(4+1)] x^(4+1) + [4/(-2+1)]x^(-2+1) + [1/(1+1)] x^(1+1)
2/5 x^5 - 4x^-1 + x^2/2
2. y = 5x^3 - 2x^-2 + 1
ReplyDeletewith respect to x:
the deferential of 5x^3 = 3(5)x^(3-1)
= 15x^2
the deferential of 2x^-2 = -2(2)x^(-2-1)
= -4x^-3
the deferential of 1 = 0
hence:
dy/dx = 15x^2 + 4x^-3
integrate with respect to x
ReplyDelete2 x^ 4 + 4/x^ 2+ x
2 x^ 4 + 4/x^ 2+ x
∫2x^4 + 4x^-2 + x dx
= ∫(2x^(4+1))/(4+1)+ (4x^ (-2+1))/ (-2+1) + (x^(1+1))/(1+1)
= ∫ ((2x^5)/5) + (4x^-1)/-1) + ((x^2)/2)
3.y= 6x^2+2 sin x
ReplyDeletedy/dx= 12x+2 cos x
when x= n/8
dy/dx= 12(n/8)+2 cos(n/8
1)
ReplyDeletey = 4x^3 - 3x^2 + 2x
dy/dx = 3(4)(x^3-1) - 2(3)(x^2-1) + 1(1)(x^1-1)
= 12x^2 - 6x + 2
2)
ReplyDeletey = 5x^3 - 2x^-2 + 1
dy/dx = 15x^2 +4x^-3
3)
ReplyDeletey = 6 x^ 2 + 2 sin x
dy/dx = 12 x + 2 cosx
when x = ñ/8
dy/dx = 12(ñ/8) + 2cos(ñ/8)
= 3/2ñ + 1.85
= 4.71 + 1.85
= 6.56
5)
ReplyDelete2 x^ 4 + 4/x^ 2+ x
2x^4 + 4x^-2 + x
[2/(4+1)] x^(4+1) + [4/(-2+1)]x^(-2+1) + [1/(1+1)] x^(1+1)
2/5 x^5 - 4x^-1 + x^2/2
6)
ReplyDelete2x^2(2x+3)
4x^3+6x^2
4x^4/4+6x^3/3
x^4+2x^3
When differentiating you must multiply the number infront of the variable by the power then minus one from the power,
ReplyDeleteie.if you have 2x^3 then the diffrential is 12x^2
if there is no power then the number infront of the variable is what the diffrential would be, ie. 2x the differential is 2
if there is only a number then it dissappears and is no longer present in the equation.
This comment has been removed by the author.
ReplyDelete1) y = 4x ^3 - 3 x^ 2 + 2x
ReplyDeletedy/dx = (4*3)x^(3-1) - (3*2)x^(2-1)+ 2
dy/dx = 12x^2 - 6x + 2
2) y = 5 x ^3 - 2 x^ -2 + 1
ReplyDeletedy/dx = (5*3)x^(3-1) - (2*-2)x^(-2-1)
dy/dx = 15x^2 + 4x^-3
3) y = 6 x^ 2 + 2 sin x
ReplyDeletedy/dx = (6*2)x^(2-1) + 2sinx
dy/dx = 12x + 2cosx
~
when x = n/8
then 12x +2cosx
=12(n/8) + 2cos(n/8)
???
HELP!!!!!!!!!!
*sigh* i'm confused!!!!
can someone who understands this please explain????? :(
1)y=4x^3-3x^2+2x
ReplyDeletedy/dx=12x^2-6x+2
2)y=5x^3-2x^-2+1
ReplyDeletedy/dx=15x^2+4x^-3
3)
ReplyDeletey=6x^2+2sinx
dy/dx=12x+2cosx
when x=n/8
dy/dx=12(n/8)+2cos(n/8)
4)
ReplyDeletev=2@^3+2cos@+sin@
dv/d@=6@^2-2sin@+cos@
5)
ReplyDelete2x^4+4x^-2+x
2x^5/5+4x^-1/-1+x^2/2+c
6)
ReplyDelete2x^2(2x+3)
4x^3+6x^2
4x^4/4+6x^3/3
x^4+2x^3
7)
ReplyDelete1+2sinx
1x-2cosx
1(45)-2cos45
45-1.414
43.586
8)2x+3cosx
ReplyDeletex^2+3sinx
using 90and60 bounds
90^2+3sin90
1803 and
60^2+3sin60
3600+2.6
3602.6
so 8103-3602.6
4500.4
This comment has been removed by the author.
ReplyDeletev = 2@^3 + 2cos@ + sin@
ReplyDeletedv/d@ = 3(2)(@^3-1) - 1 (2)(sin@) + 1(cos@)
= 6@^2 - 2sin@ + cos@
number (1)
ReplyDeletey = 4x^3 - 3x^2 + 2x
dy/dx = 3(4)(x^3-1) - 2(3)(x^2-1) + 1(1)(x^1-1)
= 12x^2 - 6x + 2
number (2)
ReplyDeletey = 5x^3 - 2x^-2 + 1
dy/dx = 15x^2 +4x^-3
number (3)
ReplyDeletey = 6 x^ 2 + 2 sin x
dy/dx = 12 x + 2 cosx
when x = ñ/8
dy/dx = 12(ñ/8) + 2cos(ñ/8)
= 3/2ñ + 1.85
= 4.71 + 1.85
= 6.56
number (4)
ReplyDeletev = 2ø^3 + 2cosø + sinø
dv/dø = 6ø^2 - 2sinø + cosø
number (5)
ReplyDelete2x^4+4x^-2+x
2x^5/5+4x^-1/-1+x^2/2+c
number (6)
ReplyDelete2x^2(2x+3)
4x^3+6x^2
4x^4/4+6x^3/3
x^4+2x^3
number (7)
ReplyDelete1+2sinx
1x-2cosx
1(45)-2cos45
45-1.414
43.586
number (8)
ReplyDelete2x+3cosx
x^2+3sinx
using 90and60 bounds
90^2+3sin90
1803 and
60^2+3sin60
3600+2.6
3602.6
so 8103-3602.6
4500.4
integration is the reverse of differentiation.
ReplyDeleteie. add one to the power then divide by the power eg. ∫5x^2 dx
=[5x(2+1)]/3
= 5x^3/3
This comment has been removed by the author.
ReplyDelete5) 2 x^ 4 + 4/x^ 2+ x
ReplyDelete=2x^4 + 4x^-2 + x
=[2x^(4+1)]/5 + 4x^(-2+1)/-1 + x^2/2
=2x^5/5 + 4x-1/-1 + x^2/2 + c
6) 2x^2 (2x+3)
ReplyDelete= 4x^3 + 6x^2
=[4x^(3+1)]/4 + [6x^(2+1)/3)
= x^4 + 2x^3 + c
This comment has been removed by the author.
ReplyDelete7) Integrate (1 + 2 sin x ) wrt x with 45 and 0 degrees as bounds
ReplyDelete(1 + 2sinx)
=1x - 2cosx + c
=[1(45)- 2cos(45)]-[1(0)- 2cos(0)
=[45 - 1.414]-[2]
= 43.586 - 2
= 41.586
8)Integrate (2x + 3 cos x ) wrt x with 90 and 60 degrees as bounds
ReplyDelete(2x + 3cosx)
=2x^(1+1)/2 + 3sinx + c
=2x^2/2 + 3sinx + c
=(90^2)+ 3sin(90) - (60^2) + 3sin(60)
= [8100 + 3] - [3600 + 2.6]
= 8103 - 3602.6
= 4500.4
Question 1.
ReplyDeletey= 4x ^3 - 3 x^ 2 + 2x
dy/dx= 12x^2 – 6x +2
Question 2.
ReplyDeletey = 5 x ^3 - 2 x^ -2 + 1
dy/dx= 15x^2 +4 x^ -3
Question 3.
ReplyDeletey = 6 x^ 2 + 2 sin x
dy/dx= 12x + 2 cos x
at x = ñ/8
dy/dx= 12 (ñ/8) + 2 cos (ñ/8)
dy/dx = 12 ñ/8 + (2 cos ñ)/8
dy/dx = 3 ñ/2 + (1 cos ñ)/4
Question 4.
ReplyDeletev = 2ø ^ 3 + 2 cos ø + sin ø
dv/d ø= 6 ø^ 2 - 2 sin ø + cos ø
Question 5.
ReplyDelete∫2 x^ 4 + 4/x^ 2+ x dx
∫2 x^ 4 + 4x^ -2+ x dx
2x^5/5 – 4x^-1 + x^2/2 + c {where c is a constant}
2/5 x^5 – 4/ x + 1/2 x^2 + c
Question 6.
ReplyDelete∫2 x ^2( 2x + 3 )
∫4x^3 + 6x^2 dx
4x^4/4 + 6x^3/3 + c {where c is a constant}
X^4 + 2x^3 + c
Question 7.
ReplyDelete∫(1 + 2 sin x ) dx
x + 2 cos x + c {where c is a constant}
For bounds 45 and 0
[45 + 2 cos 45] – [0 + 2 cos 0]
[43.586]– [2]
41.56units to 2 deci. Places
Question 8.
ReplyDelete∫(2x + 3 cos x) dx
2x^2/2 – 3 sin x + c {where c is a constant}
x^2 – 3 sin x + c
For bounds 90 and 60
[(90)^2 – 3 sin90] – [(60)^2 – 3 sin60]
8097 – 3597.40
4499.6 units to 1 deci. Place
for ques 5
ReplyDeletey=2x^4+4/x^2+x dx
y=2x^4+4x^-2+x dx
integral=2x^5/5+4x^-1+x^2/2
6.
ReplyDeleteIntegrating w.r.t. x
2 x ^2( 2x + 3 )
4x^3 + 6x^2
y = 4x^4/4 + 6x^3/3 + c
y = x^4 + 2x^3 +c
(3)
ReplyDeleteFind dy/dx at x = ñ/8 if y = 6 x^ 2 + 2 sin x
dy/dx = 12x^2 + 2cosx
x = ñ/8
dy/dx = 12( ñ/8)^2 + 2cos( ñ/8)
dy/dx = 6(ñ/8) + 2cos( ñ/8)
#1
ReplyDeletey=4x^3-3x^2+2x
dy/dx=12x^2-6x+2