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Pochodna funkcji 1/(cosx)^2

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

$f\left(x\right) =$

$\dfrac{1}{{\left(\cos\left(x\right)\right)}^{2}}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{{\left(\cos\left(x\right)\right)}^{2}}\right)}}$

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

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

$=\dfrac{-2{\cdot}\class{steps-node}{\cssId{steps-node-8}{\left(-\sin\left(x\right)\right)}}}{{\left(\cos\left(x\right)\right)}^{3}}$

$=\dfrac{2{\cdot}\sin\left(x\right)}{{\left(\cos\left(x\right)\right)}^{3}}$