Differentiation Year 13 (Chain, Quotient, Product rule)

Question 1

How do you differentiate y=a^x ?

Answer 1

dy/dx = a^xlna

Question 2

How do you differentiate y=a^f(x) ?

Answer 2

dy/dx = a^f(x) lna x f’(x)

Question 3

How do you differentiate y=lnx ?

Answer 3

dy/dx = 1/x

Question 4

How do you differentiate y=ln(f(x)) ?

Answer 4

dy/dx = 1/f(x) X f’(x)

Question 5

How do you differentiate y=e^f(x) ?

Answer 5

dy/dx = e^f(x) X f’(x)

Question 6

How do you differentiate y=cosx ?

Answer 6

dy/dx = -Sinx

Question 7

How do you differentiate y=Cos(f(x)) ?

Answer 7

dy/dx = -Sin(f(x)) X f’(x)

Question 8

How do you differentiate y=Sinx ?

Answer 8

dy/dx = Cosx

Question 9

How do you differentiate y=Sin(f(x)) ?

Answer 9

dy/dx = Cos(f(x)) X f’(x)

Question 10

Why would x =ln(-2) cause a maths error?

Answer 10

because you can only take logs of positive numbers

Question 11

What is the product rule?

Answer 11

dy/dx = u(dv/dx) + v(du/dx)

Question 12

How would you differentiate 7^x ?

Answer 12

dy/dx = 7^x ln7

Question 13

How would you differentiate ln(3x^2) ?

Answer 13

dy/dx = (1/3x^2) (6x) = 6x / 3x^2

Question 14

When do stationary points occur?

Answer 14

when dy/dx = 0

Question 15

How would you differentiate (Sin3x) ^2 ?

Answer 15

dy/dx= 2(Sin3x) X (Cos3x) (3)

Question 16

What is the Quotient Rule?

Answer 16

V(du/dx) - U(dv/dx) / V^2