Differentiation

Question 1

How do you differentiate two terms inside brackets with a power?

Answer 1

Differentiate the brackets as if the brackets are a single pronumeral.
Then multiply the entire equation by the derivative of the inside of the brackets.

Question 2

What is the product rule?

Answer 2

If y = uv

Then y’ = vu’ + uv’

Question 3

What is the quotient rule?

Answer 3

u
If y = —-
v

             vu' - uv' Then  y' = ------------
                v^2

Question 4

How do you find the gradient of a tangent using first principles?

Answer 4

f(x + h) - f(x)
m = —————–
h

f(x) = the equation of the curve