If y=xⁿ   then =nx^n-1

If y=axⁿ  then =anx^n-1   or

If f(x)=axⁿ  then f’(x)=anx^n-1

If y=sinθ   then =cosθ

If y=cosθ    then =-sinθ

If y=tanθ    then =sec²θ

If y=cotθ     then =cosec²θ

If y=secθ       then =tanθsecθ=sinθ/cos²θ

If y=cosecθ     then =-cotcosec=-cosθ/sin²θ

If y=sin^-1x/a     then =

If y=cos^-1x/a    then =

If y=tan^-1x/a     then =

If y=cot^-1x/a      then =

If y=sec^-1x/a      then =

If y=cosec^-1x/a    then =

If y=e^x                   then =e^x

If y=e^ax                 then =ae^ax

If y=a^x                   then =a^xlna

If y=ln x                  then =

Product rule

If y=uv where u and v are both functions of x, then =u +v

Quotient rule

If y=   where u and v are both functions of x, then =

Function of a function

If y is a function of x then    = ×

Successive differentiation

If y=f(x) then its first derivative is written     or f’(x)

If this expression is differentiated a second time when the second derivative is obtained and is written  or f’’(x)