Exponentials and Logarithms

Derivative of e to the x

y’ = e to the x

Derivative of complex exponential functions

y’ = f’(x) e to the power of f(x)

Applications of differentiation (exponentials base e)

To find stationary points, solve y’ = 0

To determine concavity, explore whether y’’ > 0 or y’’ < 0

To find points of inflexion y’’ = 0

To find tangents and normals to a curve

Integration of Exponential Functions and applications of Integration (Standard)

Only works when the index is a linear function

Integration of Exponential Functions and applications of Integration (Reference Sheet)

To remember, it is just the reverse of differentiating exponentials. You may need fudging.

Review of Logarithmic Functions

To remember, revise these rules.

Derivative of logarithm

Thus why if y = ln(x) y’ = 1/x

Add photos of example question on all of them to assist you in recognition.