List of Derivative Rules | All Derivative Rules

You can find all the derivative rules below. We wish everyone good work and good lessons...

Below is a list of all the derivative rules.

Constant Rule:

$f(x)=c$ then $f'(x)=0$

Constant Multiple Rule:

$g(x)=c.f(x)$ then $g'(x)=c.f'(x)$

Power Rule:

$f(x)=x^n$ then $f'(x)=nx^{n-1}$

Sum and Difference Rule:

$h(x)=f(x) ± g(x)$ then $h'(x)=f'(x) ± g'(x)$

Product Rule:

$h(x)=f(x).g(x)$ then $h'(x)=f'(x).g(x)+f(x).g'(x)$

Quotient Rule:

$h(x)=\frac{f(x)}{g(x)}$ then $h'(x)=\frac{f'(x).g(x)-f(x).g'(x)}{g(x)^2}$

Chain Rule:

$h(x)=f(g(x))$ then $h'(x)=f'(g(x)).g'(x)$

Trig Derivatives:

$f(x)=sin(x)$ then $f'(x)=cos(x)$

$f(x)=cos(x)$ then $f'(x)=-sin(x)$

$f(x)=tan(x)$ then $f'(x)=sec^2(x)$

$f(x)=sec(x)$ then $f'(x)=sec(x).tan(x)$

$f(x)=cot(x)$ then $f'(x)=-csc^2(x)$

$f(x)=csc(x)$ then $f'(x)=-csc(x).cot(x)$

Exponential Derivatives:

$f(x)=a^x$ then $f'(x)=ln(a).a^x$

$f(x)=e^x$ then $f'(x)=e^x$

$f(x)=a^{g(x)}$ then $f'(x)=ln(a).a^{g(x)}.g'(x)$

$f(x)=e^{g(x)}$ then $f'(x)=e^{g(x)}.g'(x)$

Logarithm Derivatives:

$f(x)=log_a(x)$ then $f'(x)=\frac{1}{ln(a).x}$

$f(x)=lnx$ then $f'(x)=\frac{1}{x}$

$f(x)=log_a(g(x))$ then $f'(x)=\frac{g'(x)}{ln(a).g(x)}$

$f(x)=ln(g(x))$ then $f'(x)=\frac{g'(x)}{g(x)}$