Differentiation

Chain rule

100

y=(2x+1)²

y'=4(x+1)

200

Find y'(3) when y=10(x²-3)⁶

22799360

300

Find f'(x) when f(x)=(1-4x)²

-8(1-4x)

or 32x-8

400

f(x)= 1/(x+2)

f'(x)= -1/(x+2)²

500

Find f'(-1) when f(x)=1/(4-3x)²

6/343

Product rule

100

f(x)= x(x+1)³

Find f'(x) (fully factorise me!)

f'(x)=(x+1)²(4x+1)

200

f(x)=(x-2)³(x+1)⁵

f'(x)=?

f'(x)=4(x-2)²(x+4)⁴(2x-3)

300

f(x)= x^1/2(x+3)²

Find f'(4).

f'(4)=129/4   or    32.25

400

f(x)=3x²(2x³-3x²)

f'(x)=6x⁵+3x⁴-18x³

500

Find the second derivative: 

y=4x³(x⁵+2x²)

224x⁶+160x³

Quotient rule

100

Differentiate

y=x/(x+1)

1/(x+1)²

200

Find f''(x) when f(x)=x/(x+1)

-2/(x+1)³

300

Find the stationary point for y=12/(2x+5)²

Tricked ya! No stat points here

400

Differentiate (x²+1)/e^x

−(x²−2x+1)e^−x

500

Differentiate: (x-1)²/(2x+5)

(2x+5)(x-1)(3-x)/(2x+5)²

Higher derivatives

100

Find the third derivative of x³-x²+x-1

6

200

Find the fourth derivative of 2x³+x

0

300

Find the fourth derivative of:

y=1/x

24/x⁵

400

Find the fourth derivative of x^1/3

-10x^-8/3 /27

500

Find the 6th derivative of x¹⁰

151200x⁴

Differentiate me!

100

Differentiate 4x²+(4/x²)

8x-8/x³

200

Find the values of x for which y''=0 given that,

y=x⁴-6x²+11

x=1,-1

300

Differentiate y=2xe^-x

2e^-x-2xe^-x

 

400

Find where f''(x)=0

y=x⁴+4x³+6x²+3x+2

(-1,2)

500

It is given that y = ƒ(g(x)), where ƒ(1) = 3, ƒ′(1) = −4, g(5) = 1 and g′(5) = 2. What is the value of y′ at x = 5?

-8