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

解答

\frac{d}{d x} (ln (x^{c o s (x)}))

- sin (x) ln (x) + \frac{cos ( x )}{x}

求解步骤

\frac{d}{d x} (ln (x^{c o s (x)}))

使用连锁律:

\frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

= \frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

\frac{d}{d x} (x^{c o s (x)}) = x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

= \frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

化简

\frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x}) : - sin (x) ln (x) + \frac{cos ( x )}{x}

= - sin (x) ln (x) + \frac{cos ( x )}{x}

t an g e n t x y + 1 + e = e^{- x y}, (1, - 1)

\int 6 x y^{2} d y

t an g e n t f (x) = e^{x}, at x = ln (14)

x \to 2 lim (2 x - 4 + 8)

\int (cot (x)) d x