What is the chain rule?

The chain rule is a type of differentiation used when you are differentiating a function of a function e.g. (2x+5)^3, or e.g.2. (x^2 + 5)^0.5.
Firstly you replace one function with u. You then differentiate to produce dy/du in the normal way. Then do the same to produce du/dx. To get dy/dx you must do dy/du multiplied by du/dx and replace any u's with the acutal formula. For example, if y=(2x+5)^3, then let u=2x+5. dy/du=3u^2. du/dx=2. Thus, dy/dx=2 x 3u^2 =6u^2 =6(2x+5)^2.

AS

Related Maths A Level answers

All answers ▸

f(x)=x^3 + x^2 -10x +8 show that (x-1) is a factor of f(x), Factorise f(x) fully , sketch the graph of f(x)


Solve (3x+6)/4 - (2x-6)/5 = (x+7)/8.


Differentiate y = (x^2 + 1)^1/3


(M1) What direction does friction act in? What are the friction equations both generally and in limiting equilibrium? What does it mean for a system to be in equilibrium?