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