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