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Chain rule

Total questions: 10

Worksheet time: 30mins

Name
Class
Date
1.
Find the derivative of  f(x) = (x6 + 4)5
a)
f '(x) = 5x5(x4 + 4)4
b)
f '(x) = 6x5(x6 + 4)4
c)
f '(x) = 30x5(x6 + 4)4
d)
f '(x) = 30x6(x6 + 4)4
2.
Find the derivative of f(x)=(x3-2x)2
a)
6x5 - 12x3+8x
b)
6x5 - 16x3+8x
c)
x6-4x4+4x2
d)
6x5 - 16x3-8x
3.
a)

A

b)

B

c)

C

d)

D

4.

find y' for y=(e5x)+1

a)

5e5x+1

b)

e5x

c)

5e5x

d)

1

5.

find y' for y= sin(2x2)

a)

4sin(2x2)

b)

4xcos(2x2)

c)

2xcos(2x2)

d)

xcos(4x2)

6.
a)
b)
c)
d)
7.
Find the derivative.
 f(z) = 1/(3z2) + 4z3
a)
f'(z) = 6z3 + 12z2
b)
f'(z) = 6z + 12x2
c)
f'(z) =  -2/(3z3) + 12z2
d)
f'(z) = -6/z2 + 12z2
8.

Find  dvdt if v=t+8t\frac{dv}{dt}\ if\ v=t+\frac{8}{t}  

a)

 18t21-\frac{8}{t^2}  

b)

 18t1-\frac{8}{t}  

c)

 t8t2t-\frac{8}{t^2}  

d)

 1+8t21+\frac{8}{t^2}  

9.

Find  dpdq if p=1q+9\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}  

a)

 12(q+9)32-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}  

b)

 12(q+9)32\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}  

c)

 1(q+9)32-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}  

d)

 1q+9-\frac{1}{\sqrt{q+9}}  

10.

 dydt if y=cos10t+12\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}  Find

a)

 510t+12sin10t+12\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}  

b)

 1210t+12sin10t+12\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}  

c)

 sin10t+12-\sin\sqrt{10t+12}  

d)

 sin(510t+12)-\sin\left(\frac{5}{\sqrt{10t+12}}\right)