If you're studying A Level Maths, practising differentiation is essential for developing confidence with calculus and preparing for exams. This A Level Maths derivatives worksheet gives you the opportunity to apply key differentiation rules to a variety of functions and test your understanding through practice questions.
The worksheet covers several important areas of differentiation, including trigonometric and inverse trigonometric functions, the chain rule and successive derivatives. Work through the questions independently before using the solutions to check your answers and identify any areas where you may need more practice.
What will you practise in this derivatives worksheet?
This worksheet includes exercises covering some of the key differentiation techniques studied in A Level Maths, including:
- Trigonometric differentiation – differentiating functions involving sine, cosine and other trigonometric functions.
- Inverse trigonometric functions – practising derivatives involving inverse trigonometric expressions.
- The chain rule – differentiating composite functions by applying the chain rule correctly.
- Successive derivatives – finding second and higher-order derivatives.
- Mixed differentiation problems – applying more than one differentiation technique to solve a problem.
Differentiate the function 
.
Use the product rule on both terms.
For 
: 
.
For 
: 
.
So 
.
Find 
for values of 
where it is defined.
Let 
.
Use the chain rule: if 
, then 
.
Here 
, so 
.
Therefore 
, valid when 
(so 
is defined over the reals).
Differentiate 
.
Use the product rule with 
and 
. 
, 
.
So 
.
Differentiate the composite function 
for 
.
Let 
with 
.
Then 
.
Compute 
. Also 
.
So 
.
Find 
for 
.
Use the product rule with 
, 
. 
, 
.
Therefore 
.
Differentiate 
for .
Write 
. Use the product rule: 
.
So 
.
Equivalently, with a single fraction: 
.
Differentiate 
.
Let 
.
By the chain rule, 
.
So 
.
Find 
.
Let 
with 
.
Then . Here 
.
Therefore 
.
Differentiate 
.
Use the product rule with 
and 
. 
(chain rule), and 
. So 
.
Factor 
: 
.
Find the derivative of 
.
Rewrite as 
.
Using the chain rule: 
.
Since 
, we get 
.
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