Ap Calculus AB - Unit 3 Review

chain rule

d/dx[f(x)gx)] = f’[g(x)]*g’(x)

implicit differentiation

Take the derivative like normal except for anything except any variable that is not based on x, then take derivative in context of the variable. For example, d/dx(5y²) → 10y*dy/dx

Inverse derivatives

Function must be invertible and differentiable.
If f(x)=0, then the inverse function is differentiable, and the inverse of the derivative of the original function is equal to the derivative of the inverse function.

d/dx[arcsin(u)]

u’/sqrt(1-u²)

d/dx[arccos(u)]

-u’/sqrt(1-u²)

d/dx[arctan(u)]

u’/1-u²

d/dx[arccot(u)]

-u’/1-u²

d/dx[arcsec(u)]

u’/[|u|sqrt(1-u²)]

d/dx[arccsc(u)]

u’/[|u|sqrt(1-u²)]-

y’’

d²y/d²x