derivative of ln(ln(x^{2x}))

解答

\frac{d}{d x} (ln (ln (x^{2 x})))

\frac{ln ( x ) + 1}{x ln ( x )}

求解步骤

\frac{d}{d x} (ln (ln (x^{2 x})))

使用连锁律:

\frac{1}{ln ( x ^{2 x} )} \frac{d}{d x} (ln (x^{2 x}))

= \frac{1}{ln ( x ^{2 x} )} \frac{d}{d x} (ln (x^{2 x}))

\frac{d}{d x} (ln (x^{2 x})) = 2 (ln (x) + 1)

= \frac{1}{ln ( x ^{2 x} )} \cdot 2 (ln (x) + 1)

化简

\frac{1}{ln ( x ^{2 x} )} \cdot 2 (ln (x) + 1) : \frac{ln ( x ) + 1}{x ln ( x )}

= \frac{ln ( x ) + 1}{x ln ( x )}

\int \frac{27}{x ( x ^{2} + 4 ) ^{2}} d x

\frac{d y}{d x} = ln (x^{y})

\int (x^{4} - 4^{x} + 4 x - \frac{4}{x}) d x

d er i v a t i v e y = \frac{( x + 7 )}{( x - 5 )}

\frac{d}{d x} (\frac{1}{2} \cdot ln (x))