Calculus quiz #1

Product rule

d/dx (uv) = uv’ + vu’

Quotient rule

d/dx (u/v) = (vu’ -uv’)/v²

Inverse derivative

(f^-1)’(a) = 1/(f’(f^-1(a)) OR if g(x)=f^-1(x) then g’(a)=1/(f’(g(a))

Chain rule

d/dx f(g(x)) = f’(g(x)) g’(x)

Average value of a function

1/(b-a) integral from a to b of f(x)dx

Derivative of cos

-sin

Derivative of sin

cos

derivative of tan

sec²

derivative of sec

sec tan

Derivative of cot

-csc²

Derivative of csc

-csc cot

Draw pictures of 3d shapes

Idk just wing it

Draw the unit circle

Also just wing it

Volume of sphere

4/3 pi r²

Volume of right circular cylinder

pi r² h

Frustum of a right circular cone (idk what that is)

(pi(r² + rR + R²)h)/3

Volume of a right circular cone

(pi r² h)/3 OR not right circular cone is just Ah/3 where A is the area of the base

Definition of derivative (limit things)

f’(a) = lim h→0 of (f(x-h) - f(x))/h OR at a point: lim x→a of f(x)-f(a)/(x-a)