Derivatives of Trig/Inverse Trig Functions

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec^2(x)

d/dx csc(x)

-csc(x)cot(x)

d/dx sec(x)

sec(x)tan(x)

d/dx cot(x)

-csc^2(x)

d/dx sin^-1(x)

1/√(1-x^2 )

d/dx cos^-1(x)

-1/√(1-x^2 )

d/dx tan^-1(x)

1/(1+x^2)

d/dx csc^-1(x)

-1/(|x| √(x^2-1))

d/dx sec^-1(x)

1/(|x| √(x^2-1))

d/dx cot^-1(x)

-1/(1+x^2)

MVT

f’(c)=(f(b)-f(a))/(b-a)

Linear approximation

L(x)=f(a)+f’(a)(x-a)

Differentials

dy=f’(x)dx

Limit definition of a derivative

f’(x)=lim h—>0 (f(x+h)-f(x))/h