Matematyka
$f\left(x\right) =$ | $\left({x}^{2}+1\right){\cdot}\ln\left(x\right)$ |
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$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$ |
$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\left({x}^{2}+1\right){\cdot}\ln\left(x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}+1\right)}}{\cdot}\ln\left(x\right)}}+\class{steps-node}{\cssId{steps-node-5}{\left({x}^{2}+1\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x\right)\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}{\cdot}\ln\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{x}}}{\cdot}\left({x}^{2}+1\right)$ $=\class{steps-node}{\cssId{steps-node-8}{2}}\class{steps-node}{\cssId{steps-node-9}{x}}{\cdot}\ln\left(x\right)+\dfrac{{x}^{2}+1}{x}$ |