Differentiating natural logarithms Revision Card

CalculusAdditional / Further Maths

Differentiate natural logarithms with linear arguments.

for .
For a constant multiplier, .
For a linear argument, , where .
Divide the inner derivative by the inner expression, keeping the constant multiplier.

Example 1

Differentiate with respect to . Assume .

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Differentiate with respect to . Assume .

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Remember
Check the inner derivative before simplifying your answer.

Question 1

Differentiate with respect to . Assume .

Check answer

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Question 2

Differentiate with respect to . Assume .

Check answer

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Question 3

Differentiate with respect to . Assume .

Check answer

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Question 4

Differentiate with respect to . Assume .

Check answer

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.

Question 5

Differentiate with respect to . Assume .

Check answer

Differentiate the inner expression.

Differentiate the logarithm by dividing by the inner expression. Multiply by the constant and the inner derivative.