CalculusAdditional / Further Maths

Differentiating exponentials

Differentiate natural exponentials with linear exponents.

  • , so .
  • For a linear exponent, .
  • Keep the exponent unchanged and multiply by its derivative . An added constant differentiates to .

Example 1

Differentiate with respect to .

Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.

Example 2

Differentiate with respect to .

Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.

Remember
Check the inner derivative before simplifying your answer.

Your turn

Question 1

Differentiate with respect to .

Check answer
Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.
Question 2

Differentiate with respect to .

Check answer
Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.
Question 3

Differentiate with respect to .

Check answer
Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.
Question 4

Differentiate with respect to .

Check answer
Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.
Question 5

Differentiate with respect to .

Check answer
Differentiate the inner expression.The exponential keeps the same exponent. Multiply by the constant and the inner derivative.
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