(\partial)/(\partial x)(9cos(ye^{xy})sin(x))

解答

\frac{\partial}{\partial x} (9 cos (y e^{x y}) sin (x))

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

求解步骤

\frac{\partial}{\partial x} (9 cos (y e^{x y}) sin (x))

将

y

视为常数

将常数提出:

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

= 9 \frac{\partial}{\partial x} (cos (y e^{x y}) sin (x))

使用微分乘法定则:

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

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

= 9 (\frac{\partial}{\partial x} (cos (y e^{x y})) sin (x) + \frac{\partial}{\partial x} (sin (x)) cos (y e^{x y}))

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

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

= 9 ((- sin (y e^{x y}) y^{2} e^{y x}) sin (x) + cos (x) cos (y e^{x y}))

化简

= 9 (- e^{y x} y^{2} sin (e^{y x} y) sin (x) + cos (e^{y x} y) cos (x))

a re a x^{2} - 19, 18 x

\frac{\partial}{\partial x} (1 + x \cdot ln (x y - 5))

\int 7 e^{c o s (x)} sin (x) d x

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

\frac{d}{d x} (\frac{1}{3} x^{3} + \frac{1}{2} x^{2})