Learning Enhancement Team
Worksheet:
y  ax n
This worksheet has questions about the differentiation using the power rule which allows you to differentiate equations of the form y
 ax n . Before attempting the questions below you should be familiar with the concepts in the study guide:
Differentiating y
 ax n .
Model answers to this sheet
Differentiating y
 ax n study guide
2.
3. a) e) i)
1. dy
Find dx y
 y

3 x 3
7 b) f) y

2 x j) y
 x 3 y y


4
 x
Find the gradient at the point where when y is defined by the following equations: c)

23 .
004 g) k) x

1 y
 
2 x 2 y y


0
2 x 3
9 d) h) l) y y y

1 .
 
1 x 9
 
3

2 x

4 x 3
for all of the curves defined in question 1. a) e) i) m) dy
Find dx
when y is defined by the following equations: y
 x
2
3 b) y

4
 x c)
3 y

2 x

1 y
 x
5
3 f) y

1 x 3
5 g) y
 x
5
3 x
1 y

2 y

2 x j) n) y
 y

7 x
7 x k) o) d) h) y

3
7 x l) y
 x 3 
3
2

3
 x 3
2 y

2 x y

1
5 x 3 y

4

5
3 x

4. Differentiate the following: a) Find dE dv where E

1 mv 2
2 and m is a constant b) dE
Find dP
where E

Q
P
and Q is a constant. c) dE
Find dQ
where E

Q
P
and P is a constant. d) dE
Find dm
where E
 mc 2 and c is a constant. e) Find ds dt
where s
 ut

1 at 2 and u and a are constants.
2 f) Find dv 2 ds
where v 2
 u 2

2 as and u and a are constants. g) dy
Find dx where y
 mx
 c and m and c are constants
This worksheet is one of a series on mathematics produced by the Dean of
Students' Office at the University of East
Anglia.
Scan the QR-code with a smartphone to go to the Learning Enhancement Team website .