Pochodna funkcji (x^2+1)lnx

$f\left(x\right) =$ $\left({x}^{2}+1\right){\cdot}\ln\left(x\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$

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

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

$=\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}{\cdot}\ln\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{x}}}{\cdot}\left({x}^{2}+1\right)$

$=\class{steps-node}{\cssId{steps-node-8}{2}}\class{steps-node}{\cssId{steps-node-9}{x}}{\cdot}\ln\left(x\right)+\dfrac{{x}^{2}+1}{x}$

Podziel się rozwiązaniem:

Wybrane przykłady