Kamis, 14 Mei 2015

Tabel Turunan Fungsi (Diferensial)

Berikut adalah rumus-rumus dasar turunan:

c' = 0 \,
x' = 1 \,
(cx)' = c \,
|x|' = {x \over |x|} = \sgn x, \qquad x \ne 0(x^c)' = cx^{c-1} \qquad \mbox{baik } x^c \mbox{ maupun } cx^{c-1} \mbox { terdefinisi}\left({1 \over x}\right)' = \left(x^{-1}\right)' = -x^{-2} = -{1 \over x^2}
\left({1 \over x^c}\right)' = \left(x^{-c}\right)' = -cx^{-(c+1)} = -{c \over x^{c+1}}\left(\sqrt{x}\right)' = \left(x^{1\over 2}\right)' = {1 \over 2} x^{-{1\over 2}} = {1 \over 2 \sqrt{x}}, \qquad x > 0
\left(c^x\right)' = c^x \ln c ,\qquad c > 0
\left(e^x\right)' = e^x
\left(ln x\right)' = \frac{1}{x}
    (\sin x)' = \cos x \,
    (\cos x)' = -\sin x \,
    (\tan x)' = \sec^2 x = { 1 \over \cos^2 x} \,
    (\sec x)' = \sec x \tan x \,
    (\csc x)' = -\csc x \cot x \,
    (\cot x)' = -\csc^2 x = { -1 \over \sin^2 x} \,
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