Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (copy)

Chain Rule

• If y = f(g(x)), then y’ = f’(g(x)) * g’(x) OR

• If y = y(v) and v = v(x), then dy/dx = (dy/dv)*(dv/dx)

Implicit Differentiation

• (dx/dy) = (1/(dy/dx))

• An easier way of describing implicit differentiation is that if your variable doesn’t match dx, then you need to follow it up with d(variable)/dx

Inverse Function Differentiation

• There is a simple formula in order to find the derivative of an inverse function.

Inverse Trigonometry

• This is going to be one that is easier to just memorize, but you can also find them by following the formulas explained in implicit differentiation and using trigonometry rules.

HINTS

• When two terms are multiplied together, use product rule unless it’s easier to multiply it out

• If you see a function within another function, you will almost certainly have to use chain rule

• If there are x and y terms mixed together, we will need to use implicit differentiation

• If you’re finding the derivative at a point, just plug it in and avoid the solving out

• When evaluating derivatives at a point, look to see if the terms become one or zero

• You can mentally take certain derivatives

• If it is required to take a second derivative, simplify the first derivative before you start