Derivada de un monomio

Calculadora de Derivadas • ¡Con pasos!

Derivadas básicas

f(x)

$k$

$kx$

f’(x)

$0$

$k$

Derivadas

f(x)

$f(x)^n$

$f(x)·g(x)$

$f(x)+g(x)$

$a^{f(x)}$

$log_n(f(x))$

f’(x)

$n·f(x)^{n-1}·f'(x)$

$f'(x)·g(x)+f(x)·g'(x)$

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

$a^{f(x)}·ln(a)·f'(x)$

${\displaystyle\frac{f'(x)}{f(x)·ln(n)}=\frac{f'(x)}{f(x)}·log_a(e)}$

Versiones más complejas

f(x)

$f(x)·g(x)·h(x)$

$f(x)^{g(x)}$

f’(x)

$f'(x)·g(x)·h(x)+f(x)·g'(x)·h(x)+f(x)·g(x)·h'(x)$

$g(x)·f(x)^{g(x)-1}·f'(x)+f(x)^{g(x)}·ln(f(x))·g'(x)$

Recordar

${\displaystyle\frac{1}{f(x)}=f(x)^{-1}}$

$^n√f(x)^m=f(x)^{\frac{m}{n}}$

$ln(e)=1$

Derivadas trigonométricas

f(x)

$sen(f(x))$

$cos(f(x))$

$tg(f(x))$

$arcsen(f(x))$

$arccos(f(x))$

$arctg(f(x))$

f’(x)

$cos(f(x))·f'(x)$

$-sen(f(x))·f'(x)$

${\displaystyle f'(x)·(1+tg^2(f(x)))=\frac{f'(x)}{cos^2(f(x))}}$

${\displaystyle\frac{f'(x)}{√(1-f(x)^2)}}$

${\displaystyle-\frac{f'(x)}{√(1-f(x)^2)}}$

${\displaystyle\frac{f'(x)}{1-f(x)^2}}$