9. Differentiation

Differentiating sinx and cosx

Differentiating sinx from first principles

Differentiating when the coefficient of x is not just 1

Finding stationary points

Differentiating exponentials and logarithms

Differentiating a^x

Harder examples

The chain rule:

Example of the chain rule:

The chain rule with trig:

Writing the chain rule using function notation:

Finding the gradient at a point using the chain rule:

Implicit differentiation:

Example of implicit differentiation

The product rule:

Example of the product rule:

Harder example of the product rule:

The quotient rule:

Example of the quotient rule:

Finding stationary points using the quotient rule

where u= sinx and v=e^2x

u’=cosx v’=2e^2x

Differentiating trigonometric functions (tanx):

More examples when differentiating tan:

‘Show that’ differentiation with cosec:

Harder examples:

‘Show that’ implicit differentiation:

Parametric differentiation:

Example of parametric differentiation:

Example of parametric equation with trigonometry: (part a)

Example of parametric equation with trigonometry (part b)

Implicit differentiation:

Example of implicit differentiation:

Finding the gradient at a point with implicit differentiation:

Harder example of finding the gradient at a point with implicit differentiation:

Using second derivatives:

Finding the interval on a function:

‘Show that’ question for second derivatives:

Point of inflection:

Example of second derivative (part a):

Example of second derivative (part b):

Rates of change:

Example of rates of change:

Harder example of rates of change (part a):

Harder example of rates of change (part b):

Finding differential equations:

Harder example of differential equations:

Another example of differential equation: