(\partial)/(\partial x)(2x^4+5y^2+xy)

解答

\frac{\partial}{\partial x} (2 x^{4} + 5 y^{2} + x y)

8 x^{3} + y

求解步骤

\frac{\partial}{\partial x} (2 x^{4} + 5 y^{2} + x y)

将

y

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (2 x^{4}) + \frac{\partial}{\partial x} (5 y^{2}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= 8 x^{3} + 0 + y

化简

= 8 x^{3} + y

\int \frac{3}{x} + 10 sec^{2} (x) + 40 e^{x} d x

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

y^{^{'}} - \frac{3}{x ^{2}} y = \frac{1}{x ^{2}}

y^{^{'}} = \frac{t}{t ^{2} y + y}

n = 1 \sum \infty n e^{- \frac{n}{8}}