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Pochodna funkcji (sqr(x))/(x+1)

$f\left(q, r, s, x\right) =$	$\dfrac{qrsx}{x+1}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(q, r, s, x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{qrsx}{x+1}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{qrs{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{x}{x+1}\right)}}}}$ $=qrs{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-6}{\left(x+1\right){\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}-\class{steps-node}{\cssId{steps-node-8}{\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x+1\right)}}{\cdot}x}}}{\class{steps-node}{\cssId{steps-node-4}{{\left(x+1\right)}^{2}}}}$ $=\dfrac{qrs{\cdot}\left(\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\left(x+1\right)-\class{steps-node}{\cssId{steps-node-10}{1}}x\right)}{{\left(x+1\right)}^{2}}$ $=\dfrac{qrs}{{\left(x+1\right)}^{2}}$ Wynik alternatywny: $=\dfrac{qrs}{x+1}-\dfrac{qrsx}{{\left(x+1\right)}^{2}}$

$f\left(q, r, s, x\right) =$

$\dfrac{qrsx}{x+1}$

Note: Your input has been rewritten/simplified.

$\dfrac{\mathrm{d}\left(f\left(q, r, s, x\right)\right)}{\mathrm{d}x} =$

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{qrsx}{x+1}\right)}}$

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

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

$=\dfrac{qrs{\cdot}\left(\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\left(x+1\right)-\class{steps-node}{\cssId{steps-node-10}{1}}x\right)}{{\left(x+1\right)}^{2}}$

$=\dfrac{qrs}{{\left(x+1\right)}^{2}}$

Wynik alternatywny:

$=\dfrac{qrs}{x+1}-\dfrac{qrsx}{{\left(x+1\right)}^{2}}$