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

解答

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

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

求解步骤

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

将

y

视为常数

使用微分乘法定则:

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

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

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

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

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

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

化简

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