How do I use the chain rule for differentiation?

The chain rule is used when we have a function in the form f(g(x)).

For example sin(x^3). [In this case, f(x) = sin(x) and g(x) = x^3]

The chain rule says that the derivative of f(g(x)) is g'(x)*f'(g(x)). 

For our example:

g'(x) = 3x^2 and f'(x) = cos(x). So the derivative will be 3x^2*cos(x^3).

TK

Related Maths A Level answers

All answers ▸

How do you integrate the equation x^2 + 4x + 3 dx? (


Write down the coordinates of the centre and the radius of the circle with equation x^2+y^2-4x-8y+11=0


How to sketch a cubic function


Use the addition formulas: sin(x+y)=sin(x)*cos(y)+sin(y)*cos(x), cos(x+y)=cos(x)*cos(y)-sin(x)*sin(y) to derive sin(2x), cos(2x), sin(x)+sin(y).