Odvodi elementarnih funkcij

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Funkcija Odvod
f(x) = c f'(x) = 0
f(x) = xc f'(x) = cxc − 1
f(x) = cx f'(x) = cxlnc
f(x) = ex (e je Eulerjevo število) f'(x) = ex
f(x) = logax f'(x) = \frac{1}{x \cdot \ln{a} }
f(x) = lnx f'(x) = \frac{1}{x}
f(x) = sinx f'(x) = cosx
f(x) = cosx f'(x) = − sinx
f(x) = \operatorname{tg}x f'(x) = \frac{1}{\cos^2{x}}
f(x) = \operatorname{cotg}x f'(x) = -\frac{1}{\sin^2{x}}
f(x) = arcsinx f'(x) = \frac{1}{\sqrt{1-x^2} }
f(x) = arccosx f'(x) = -\frac{1}{\sqrt{1-x^2} }
f(x) = \operatorname{arctg} x f'(x) = \frac{1}{1+x^2}
f(x) = \operatorname{arccotg} x f'(x) = -\frac{1}{1+x^2}
f(x) = \operatorname{sinh}x f'(x) = \operatorname{cosh} x
f(x) = \operatorname{cosh} x f'(x) = \operatorname{sinh}x
f(x) = \operatorname{tgh} x f'(x) = \frac{1}{\operatorname{cosh}^2 x}
f(x) = \operatorname{cotgh} x f'(x) = - \frac{1}{\operatorname{sinh}^2 x}
f(x) = \operatorname{arcsinh} x f'(x) = \frac{1}{\sqrt{1 + x^2}}
f(x) = \operatorname{arccosh} x f'(x) = \frac{1}{\sqrt{x^2 - 1}}
f(x) = \operatorname{arctgh} x f'(x) = \frac{1}{1 - x^2}
f(x) = \operatorname{arccotgh} x f'(x) = - \frac{1}{1 - x^2}

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