Differentiate the following

Chain Rule

How would you differentiate y = (x3+3)2

Chain ruleO If you have a function within a

function then we need to use the chain rule

If y = [f(x)]n then let u = f(x) and y = un

then,

DifferentiateO y = (4x3 – 7x)6

Differentiate

𝑦=1

√𝑥2+5

Find the equation of the tangent of y = (4x + 2)4 at the point (2, 1000)

Easier way?

Do we have to use the chain rule?

O There is a quicker way to differentiate functions of functions than using the chain rule

O What is it?

O y = (x+2)2 differentiates to 2(x+2)

O y = (x2 +1)2 differentiates to 4x(x2+1)

O y = (x2 + 2x)3 differentiates to 3(2x+2)(x2+2x)2

O Can you see the rule?

RuleO If y = [f(x)]n then

Differentiate y = (3x4 + 5)5

Differentiate

Find the value of dy/dx at (2, 1/3) if