(\partial)/(\partial x)(x^2sin(3x-2y))

解答

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

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

求解步骤

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

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

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

\frac{\partial}{\partial x} (sin (3 x - 2 y)) = cos (3 x - 2 y) \cdot 3

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

x \to a lim (g (x))

y^{^{''}} + y = t

y^{^{''}} - 4 y^{^{'}} - 5 y = 9 e^{2} t

\int r cos (r) d r

t an g e n t \frac{2}{5 x + 3}, at x = - 1