Derivatives Memorization

d/dx of n

0

d/dx of x

1

d/dx of xⁿ

nx^n-1

d/dx of e^x

e^x

d/dx ln(x)

1/x

d/dx n^x

n^xln(x)

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec²(x)

d/dx cot(x)

-csc²(x)

d/dx sec(x)

sec(x)tan(x)

d/dx csc(x)

-csc(x) cot(x)

d/dx arcsin(x)

\frac{1}{\sqrt{1-x^2}}

d/dx arccos(x)

-rac{1}{ ext{sqrt}(1-x^2)}}

d/dx arctan(x)

rac{1}{1+x^2}

d/dx arc cot(x)

-rac{1}{1+x^2}

d/dx arc sec(x)

rac{1}{|x| ext{sqrt}(x^2-1)}}

d/dx arc csc(x)

-\frac{1}{|x|\sqrt{x^2-1}}