derivative of ln(xtan(x))

解答

\frac{d}{d x} (ln (x) tan (x))

\frac{tan ( x )}{x} + sec^{2} (x) ln (x)

求解步骤

\frac{d}{d x} (ln (x) tan (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = tan (x)

= \frac{d}{d x} (ln (x)) tan (x) + \frac{d}{d x} (tan (x)) ln (x)

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

\frac{1}{x} tan (x) = \frac{tan ( x )}{x}

= \frac{tan ( x )}{x} + sec^{2} (x) ln (x)

\frac{d}{d x} (x^{4} - 17 x^{2} + 16)

\int (ln (x) + 1) e^{x l n (x)} d x

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

x \to 3 lim (2 x^{2} + 1)

\frac{d}{d x} (3 x^{2} + 4 x + 2)