derivative of e^{sqrt(x^2+y^2)}

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (0.005 x^{2} - ln (x^{16}) + 70)

d er i v a t i v e y = \frac{6 x ^{2} + 8 x + 2}{x}

d er i v a t i v e - 4 x^{\frac{1}{2}}

s im pl i f y \frac{x}{2} ln (\frac{1 + x}{1 - x}) - 1

\frac{\partial}{\partial x} ((x - 1) y^{2} e^{x y})