derivative of e^{x^2y}-2x-2y

解答

\frac{d}{d x} (e^{x^{2} y} - 2 x - 2 y)

e^{x^{2} y} (2 x y + \frac{d y}{d x} x^{2}) - 2 - 2 \frac{d y}{d x}

求解步骤

\frac{d}{d x} (e^{x^{2} y} - 2 x - 2 y)

使用微分加减法定则:

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

= \frac{d}{d x} (e^{x^{2} y}) - \frac{d}{d x} (2 x) - \frac{d}{d x} (2 y)

\frac{d}{d x} (e^{x^{2} y}) = e^{x^{2} y} (2 x y + \frac{d y}{d x} x^{2})

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (2 y) = 2 \frac{d y}{d x}

= e^{x^{2} y} (2 x y + \frac{d y}{d x} x^{2}) - 2 - 2 \frac{d y}{d x}

\int x^{3} e^{12 x} d x

\frac{d}{d x} ((x^{4} + 3 x)^{- 1})

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

f (x) = \frac{5}{x ^{5}}

t a y l or f (x) = sin (x), 0