gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji x+3arctan(2x)

Pochodna funkcji x+3arctan(2x)

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

$f\left(x\right) =$

$3{\cdot}\arctan\left(2x\right)+x$

Note: Your input has been rewritten/simplified.

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

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

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

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

$=\dfrac{3{\cdot}\class{steps-node}{\cssId{steps-node-6}{2}}}{4{x}^{2}+1}+1$

$=\dfrac{6}{4{x}^{2}+1}+1$