derivative of x^y+y^x

解答

\frac{d}{d x} (x^{y} + y^{x})

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

求解步骤

\frac{d}{d x} (x^{y} + y^{x})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

t an g e n t f (x) = x^{3} - 3 x + 2, at x = 3

n = 1 \sum \infty 7 (\frac{1}{10})^{n}

\frac{d}{d x} (sin (1 - x))

in v erse l a pl a ce \frac{1}{( s + 5 ) ^{2}}

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - x ^{3} + 2}{x ^{2}})