gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji sin3x+arccos(x^2)

Pochodna funkcji sin3x+arccos(x^2)

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

$f\left(x\right) =$

$\arccos\left({x}^{2}\right)+\sin\left(3\right){\cdot}x$

Note: Your input has been rewritten/simplified.

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

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

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

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

$=\sin\left(3\right)-\dfrac{\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}}{\sqrt{1-{x}^{4}}}$