C4- Differentiation

Question 1

How do you differentiate a relationship that’s described parametrically?

Answer 1

dy/dx= (dy/dt) / (dx/dt)

Question 2

Implicit differentiation by the chain rule

Answer 2

d/dx (y^n)= (ny^(n-1)) (dy/dx)

Question 3

Implicit differentiation by the product rule

Answer 3

d/dx (xy)= x(dy/dx) + y

Question 4

What is the differential of f(y) with respect to x?

Answer 4

(f’(y))(dy/dx)

Question 5

What is the differential of f(y)g(x)?

Answer 5

g(x)f’(y)(dy/dx) + f(y)g’(x)

Question 6

If y=a^x

Answer 6

dy/dx = (a^x)lna