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Pochodna funkcji arctanx+lncosx+x^4

$f\left(x\right) =$	$\ln\left(\cos\left(x\right)\right)+\arctan\left(x\right)+{x}^{4}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(\cos\left(x\right)\right)+\arctan\left(x\right)+{x}^{4}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(\cos\left(x\right)\right)\right)}}+\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\arctan\left(x\right)\right)}}+\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{4}\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-9}{4}}\class{steps-node}{\cssId{steps-node-10}{{x}^{3}}}+\class{steps-node}{\cssId{steps-node-8}{\dfrac{1}{{x}^{2}+1}}}+\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{\cos\left(x\right)}}}{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-11}{-\sin\left(x\right)}}}{\cos\left(x\right)}+\dfrac{1}{{x}^{2}+1}+4{x}^{3}$

$f\left(x\right) =$

$\ln\left(\cos\left(x\right)\right)+\arctan\left(x\right)+{x}^{4}$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(\cos\left(x\right)\right)+\arctan\left(x\right)+{x}^{4}\right)}}$

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

$=\class{steps-node}{\cssId{steps-node-9}{4}}\class{steps-node}{\cssId{steps-node-10}{{x}^{3}}}+\class{steps-node}{\cssId{steps-node-8}{\dfrac{1}{{x}^{2}+1}}}+\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{\cos\left(x\right)}}}{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}$

$=\dfrac{\class{steps-node}{\cssId{steps-node-11}{-\sin\left(x\right)}}}{\cos\left(x\right)}+\dfrac{1}{{x}^{2}+1}+4{x}^{3}$