(\partial)/(\partial y)(e^y(x^2-y^2))

解答

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

e^{y} (x^{2} - y^{2}) - 2 e^{y} y

求解步骤

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

将

x

视为常数

使用微分乘法定则:

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

f = e^{y}, g = x^{2} - y^{2}

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

\frac{\partial}{\partial y} (e^{y}) = e^{y}

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

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

化简

= e^{y} (x^{2} - y^{2}) - 2 e^{y} y

\frac{d}{d x} (\frac{4 x ^{2} + 8 x + 4}{x})

d er i v a t i v e tan (x^{π})

a re a 3 x^{2} + 12, 4 x + 4, - 3, 3

\int e^{x^{2} + x} d x

x \to 3 lim (5 x^{2} - 3 x + 5)