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