Tabel cu derivate
Asteptati un moment. Formulele se incarca...
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$$ (x)' = 1$$
$$ (x^n)' = nx^{n-1}$$
$$ \Big({1\over x}\Big)' = -{1\over x^2}$$
$$ \Big({1\over x^n}\Big)' = -{n\over x^{n+1}}$$
$$ (\sqrt{x})' = {1\over2\sqrt{x}}$$
$$ (\sin x)' = \cos x$$
$$ (\cos x)' = -\sin x$$
$$ (\tan x)' = {1\over\cos^2x} = 1 + \tan^2x$$
$$ (\cot x)' = {1\over\sin^2x}=-(1+\cot^2x)$$
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$$ (\arcsin x)' = {1\over\sqrt{1-x^2}}$$
$$ (\arccos x)' = -{1\over\sqrt{1-x^2}}$$
$$ (\arctan x)' = {1\over 1+x^2}$$
$$ (\mathrm{arccot}\, x)' = -{1\over 1+x^2}$$
$$ (e^x)' = e^x$$
$$ (\mathrm{ln}\,x)' ={1\over x},a$$
$$ (a^x)' = a^x\mathrm{ln}\,a$$
$$ (\mathrm{log}_ax)' = {1\over x\mathrm{ln}a}$$
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Reguli de derivare
$$1.\; (\alpha * f)' = \alpha * f' \; , \; \alpha \in R$$
$$2.\; (f\pm g)' = f' \pm g'$$
$$3.\; (f*g)' = f'*g + f*g'$$
$$4.\; (f*g*h)' = f'*g*h+f*g'*h+f*g*h'$$
$$5.\; (f^n)' = n*f^{n-1}*f'$$
$$6.\; (f \circ g)' = f'(g)*g'$$