(\partial)/(\partial x)(7e^{xy}ln(x^2+y^2))

解答

\frac{\partial}{\partial x} (7 e^{x y} ln (x^{2} + y^{2}))

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

求解步骤

\frac{\partial}{\partial x} (7 e^{x y} ln (x^{2} + y^{2}))

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{\partial}{\partial x} (e^{x y} ln (x^{2} + y^{2}))

使用微分乘法定则:

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

f = e^{x y}, g = ln (x^{2} + y^{2})

= 7 (\frac{\partial}{\partial x} (e^{x y}) ln (x^{2} + y^{2}) + \frac{\partial}{\partial x} (ln (x^{2} + y^{2})) e^{x y})

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

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

= 7 (e^{x y} y ln (x^{2} + y^{2}) + \frac{2 x}{x ^{2} + y ^{2}} e^{x y})

分式相乘:

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

= 7 (e^{x y} y ln (x^{2} + y^{2}) + \frac{2 e ^{x y} x}{x ^{2} + y ^{2}})

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

in v erse l a pl a ce \frac{1}{2 s + 4}

a re a f (x) = x^{2} - 3, g (x) = 5 - x^{2}

d er i v a t i v e f (x) = 6 + 4 x

d er i v a t i v e e^{x + 4} + 8