(\partial)/(\partial y)(xye^{sin(pixy)})

解答

\frac{\partial}{\partial y} (x y e^{s i n (π x y)})

x (e^{s i n (π x y)} + π e^{s i n (π x y)} x y cos (π x y))

求解步骤

\frac{\partial}{\partial y} (x y e^{s i n (π x y)})

将

x

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (y e^{s i n (π x y)})

使用微分乘法定则:

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

f = y, g = e^{s i n (π x y)}

= x (\frac{\partial}{\partial y} (y) e^{s i n (π x y)} + \frac{\partial}{\partial y} (e^{s i n (π x y)}) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (e^{s i n (π x y)}) = e^{s i n (π x y)} cos (π x y) π x

= x (1 \cdot e^{s i n (π x y)} + e^{s i n (π x y)} cos (π x y) π x y)

化简

= x (e^{s i n (π x y)} + π e^{s i n (π x y)} x y cos (π x y))

a re a y = 2, y = sec (x)

\frac{d}{d t} (sin^{2} (π t))

\frac{d}{d x} (\frac{1}{x ^{2} + y ^{2} + z ^{2}})

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

d er i v a t i v e \frac{- 40}{x ^{7}}