gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji 5^ln(2*x)

Pochodna funkcji 5^ln(2*x)

$f\left(x\right) =$	${5}^{\ln\left(x\right)+\ln\left(2\right)}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({5}^{\ln\left(x\right)+\ln\left(2\right)}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\ln\left(5\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{{5}^{\ln\left(x\right)+\ln\left(2\right)}}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x\right)+\ln\left(2\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x\right)\right)}}{\cdot}\ln\left(5\right){\cdot}{5}^{\ln\left(x\right)+\ln\left(2\right)}$ $=\ln\left(5\right){\cdot}\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{x}}}{\cdot}{5}^{\ln\left(x\right)+\ln\left(2\right)}$ $=\dfrac{\ln\left(5\right){\cdot}{5}^{\ln\left(x\right)+\ln\left(2\right)}}{x}$

$f\left(x\right) =$

${5}^{\ln\left(x\right)+\ln\left(2\right)}$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({5}^{\ln\left(x\right)+\ln\left(2\right)}\right)}}$

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

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

$=\ln\left(5\right){\cdot}\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{x}}}{\cdot}{5}^{\ln\left(x\right)+\ln\left(2\right)}$

$=\dfrac{\ln\left(5\right){\cdot}{5}^{\ln\left(x\right)+\ln\left(2\right)}}{x}$