(\partial)/(\partial x)(x^2sin(3xy))

解答

\frac{\partial}{\partial x} (x^{2} sin (3 x y))

2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}

求解步骤

\frac{\partial}{\partial x} (x^{2} sin (3 x y))

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 = sin (3 x y)

= \frac{\partial}{\partial x} (x^{2}) sin (3 x y) + \frac{\partial}{\partial x} (sin (3 x y)) x^{2}

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

\frac{\partial}{\partial x} (sin (3 x y)) = cos (3 x y) \cdot 3 y

= 2 x sin (3 x y) + cos (3 x y) \cdot 3 y x^{2}

\int sin (3 x + 1) d x

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

\int \frac{5 x ^{3}}{6 + x ^{2}} d x

\frac{d}{d x} (2 sin (2 x))

\frac{d ^{4}}{d x ^{4}} (\frac{1}{x ^{2}})