Slide 1

“Teach A Level Maths”
Vol. 2: A2 Core Modules

5: More Chain Rule

© Christine Crisp


Slide 2

The Chain Rule
Using Composite Functions to Find the Gradient of ef(x)

Let

u = x2 then

Now use the
chain rule
dy

y = 3eu
dy
dx



dy
du



du
dx

means the gradient of the y/u function

du

du
dx

means the gradient of the u/x function

dy

 3e

u

du

du
dx

 2x


Slide 3

The Chain Rule
dy

 3e

du

u

dx

du

dy



dx

dy

 2x



du

du

Quick Method To Find The Gradient
y = ef(x)

dx

du
dx

dy
dx



dy
du



du
dx

= 3eu  2x



f '(x) ef(x)


Slide 4

The Chain Rule

Gradient of power  the original question
dy
dx



(8 x )


Slide 5

The Chain Rule
Using Composite Functions to Find the Gradient of lnf(x)

Ex.1 y = ln(3x2 + 4x)
let u = 3x2 + 4x
dy

so
du





dx
dy
dx

dy
du



A simple expression

 6x+4

dx

du
dy

y = ln(u)



du



dx

(6x+4)

G ra d ie n t o f b ra ck e t
b ra ck e t



6x  4
3x  4 x
2