gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji (lnx)^3

Pochodna funkcji (lnx)^3

$f\left(x\right) =$	${\left(\ln\left(x\right)\right)}^{3}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\ln\left(x\right)\right)}^{3}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{3}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{{\left(\ln\left(x\right)\right)}^{2}}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x\right)\right)}}$ $=3{\cdot}\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{x}}}{\cdot}{\left(\ln\left(x\right)\right)}^{2}$ $=\dfrac{3{\cdot}{\left(\ln\left(x\right)\right)}^{2}}{x}$

$f\left(x\right) =$

${\left(\ln\left(x\right)\right)}^{3}$

$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\ln\left(x\right)\right)}^{3}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{3}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{{\left(\ln\left(x\right)\right)}^{2}}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x\right)\right)}}$

$=3{\cdot}\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{x}}}{\cdot}{\left(\ln\left(x\right)\right)}^{2}$

$=\dfrac{3{\cdot}{\left(\ln\left(x\right)\right)}^{2}}{x}$