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Tabel cu derivate

Asteptati un moment. Formulele se incarca...
 $$(x)' = 1$$ $$(x^n)' = nx^{n-1}$$ $$\Big({1\over x}\Big)' = -{1\over x^2}$$ $$\Big({1\over x^n}\Big)' = -{n\over x^{n+1}}$$ $$(\sqrt{x})' = {1\over2\sqrt{x}}$$ $$(\sin x)' = \cos x$$ $$(\cos x)' = -\sin x$$ $$(\tan x)' = {1\over\cos^2x} = 1 + \tan^2x$$ $$(\cot x)' = {1\over\sin^2x}=-(1+\cot^2x)$$ $$(\arcsin x)' = {1\over\sqrt{1-x^2}}$$ $$(\arccos x)' = -{1\over\sqrt{1-x^2}}$$ $$(\arctan x)' = {1\over 1+x^2}$$ $$(\mathrm{arccot}\, x)' = -{1\over 1+x^2}$$ $$(e^x)' = e^x$$ $$(\mathrm{ln}\,x)' ={1\over x},a$$ $$(a^x)' = a^x\mathrm{ln}\,a$$ $$(\mathrm{log}_ax)' = {1\over x\mathrm{ln}a}$$
Reguli de derivare

$$1.\; (\alpha * f)' = \alpha * f' \; , \; \alpha \in R$$ $$2.\; (f\pm g)' = f' \pm g'$$ $$3.\; (f*g)' = f'*g + f*g'$$ $$4.\; (f*g*h)' = f'*g*h+f*g'*h+f*g*h'$$ $$5.\; (f^n)' = n*f^{n-1}*f'$$ $$6.\; (f \circ g)' = f'(g)*g'$$

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