(\partial)/(\partial x)(4x^2cos(xy))

解答

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

4 (2 x cos (x y) - x^{2} y sin (x y))

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用微分乘法定则:

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

f = x^{2}, g = cos (x y)

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

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

\frac{\partial}{\partial x} (cos (x y)) = - sin (x y) y

= 4 (2 x cos (x y) + (- sin (x y) y) x^{2})

化简

= 4 (2 x cos (x y) - x^{2} y sin (x y))

\frac{d}{d x} (\frac{20 x}{( x ^{2} - 4 ) ^{2}})

\int \frac{6}{x ^{2} - 4} d x

y^{^{'}} = b (1 - y) y

d er i v a t i v e 247 x - 19 x^{2}

\int {y (2 a x + b y)} d x