Derivative and Integral Rules

f(x)g'(x) + g(x)f'(x)

product rule

d/dx [f(x)/g(x)] =

quotient rule

d/dx [x^n] =

power rule

f'(g(x))g'(x)

chain rule

e^x

d/dx [ln|x|] =

d/dx [a^x] =

d/dx [log_a X] =

- sinx

secxtanx

- cscxcotx

d/dx [tanx]

d/dx [cotx]

cosx

quotient rule

derivative of a power

chain rule

derivative of an exponential function

derivative of a natural log

d/dx [a^x]

derivative of a log base a

d/dx [sinx]

d/dx [cscx]

d/dx [cosx]

d/dx [secx]

d/dx [tanx]

d/dx [cotx]

d/dx [arcsinx]

d/dx [arccscx]

d/dx [arccosx]

d/dx [arcsecx]

d/dx [arccotx]

product rule

∫dx

∫uⁿ du

∫e^u du

∫b^u*ln(b) du

∫b^u du

∫cosu du

∫-sinu du

∫sinu du

∫sec²u du

∫-cscu*cotu du

∫cscu*cotu du

∫secu*tanu du

∫-csc²u du

∫csc²u du

∫du/√(1-u²)

∫-du/√(1-u²)

∫du/(1+u²)

∫-du/u√(1-u²)

∫du/u√(1-u²)

∫-du/(1+u²)

∫du/u

∫tan u du

-ln|cos u|+C

∫cot u du

ln|sin u|+C

∫sec u du

ln|sec u+tan u|+C

∫csc u du

-ln|csc u+ cot u|+C