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Worksheetschain rule differentiation
Total questions: 20
Worksheet time: 2hrs 40mins
Name
Class
Date
1.
When do you use the chain rule?
a)
anytime you want
b)
when there is a function in a function
c)
where there are multiple layers to a lasagna (yum)
d)
when there is division
2.
What rule should be used in deriving h(x) = 2(x - 4)3
a)
Power rule
b)
Product rule
c)
Quotient rule
d)
Chain rule
3.
Find the derivative of
f(x) = (x6 + 4)5
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
4.
Find the derivative of:
f(x) = (x2 +1)6
f(x) = (x2 +1)6
a)
12(x2 + 1)6
b)
12x(x2 + 1)6
c)
12x(x2 + 1)5
d)
12(x2 + 1)5
5.
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
6.
Differentiate f(x) = (9 - 4x2)-1
a)
8x/(9 - 4x2)-2
b)
8x/(9 - 4x2)2
c)
-8x/(9 - 4x2)-2
d)
-8x(9 - 4x2)2
7.
find y' for y= (2x+1)10
a)
10(2x+1)9
b)
20(2x-1)9
c)
20(2x+1)10
d)
20(2x+1)9
8.
If f(x)=(6x2-5x)7
what is f'(x)?
what is f'(x)?
a)
7(6x2-5x)6
b)
7(6x2-5x)6⋅(12x)
c)
7(6x2-5x)6⋅(12x-5)
d)
(12x-5)
9.
Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x5 + 5)2
f(x) = (5x5 + 5)2
a)
y = 500x + 400
b)
y = 100x + 400
c)
y = -500 x - 400
d)
y = 500x - 400
10.
Find the derivative of:
f(x) = 7(3x + 4)5
f(x) = 7(3x + 4)5
a)
35(3x + 4)5
b)
35(3x + 4)4
c)
105(3x + 4)5
d)
105(3x + 4)4
11.
a)
b)
c)
d)
12.
a)
A
b)
B
c)
C
d)
D
13.
a)
b)
c)
d)
14.
Differentiate:
f(x) = x7 (5 + 8x)3
f(x) = x7 (5 + 8x)3
a)
f '(x) = x2 (5 + 8x)6 (35 + 80x)
b)
f '(x) = x6 (5 + 8x)2 (35 + 80x)
c)
f '(x) = 8x7 (5 + 8x)2 (35 + 80x)
d)
f '(x) = x6 (5 + 8x)3 (35 + 80x)
15.
Differentiate sin3x
a)
3sin2x
b)
3sin2xcosx
c)
cos3x
d)
3sinxcosx
16.
Differentiate cos(x2+x)
a)
(-2x-1)sin(x2+x)
b)
-sin(x2+x)
c)
(-2x+1)sin(x2+x)
d)
-sin(x2+x)cos(x2+x)
17.
Differentiate sin(2x-2)
a)
2cos(2x-2)
b)
cos(2x-2)
c)
2sin(2x-2)cos(2x-2)
d)
2sin(2x-2)
18.
Differentiate ln(sinx)
a)
secx
b)
cosecx
c)
1
d)
cotx
19.
Differentiate ln(cos3x)
a)
3sec3x
b)
tan3x
c)
sec3x
d)
-3tan3x
20.
Differentiate sin3xcosx
a)
3sin2xcosx+sin4x
b)
3sin2xcosx-sin4x
c)
3cos2xsin2x-sin4x
d)
3cos2xsin2x+sin4x
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