Things I need to memorize for Calc

Calc

Inverse Differentiation

1/f’[f^-1(x)]

inverse derivative of sin

1/sqrt(1-x²)

inverse derivative of cos

-1/sqrt(1-x²)

inverse derivative of tan

1/1+x²

inverse derivative of cot

-1/1+x²

inverse derivative of sec

1/|x| sqrt(1+x²)

inverse derivative of cosec

-1/|x| sqrt(1+x²)

Derivative of sin

cos(x)

Derivative of Cos

-sin(x)

Derivative of tan

sec²(x)

Derivative of Cot

cossec²(x)

Derivative of sec

sec(x)tan(x)

Derivative of cosec(x)

Cosec(x)Cotan(x)

mean value theorem

f’(x)= f(b)-f(a)/b-a

2nd FTC

if f(x) integral has another function, g(x),
derivative of integrated f(x)= f(g(x))*g’(x)

f’’(x)>0

Abs Minimum

f’’(x)<0

Abs Maximum

Trapezoid Sum

f(a)+f(b)/2 * delta x

Equilateral Triangle

sqrt3/4 s²

Isoceles Triangle

½ s²

Semicircle

½ pir²

Perpendicular cross section

s= Right-left

Vertical Cross section

s= Top - botton

Radius

f(x)-g(x)/2