(\partial)/(\partial x)(x^3y+12x^2-64y)

解答

\frac{\partial}{\partial x} (x^{3} y + 12 x^{2} - 64 y)

3 x^{2} y + 24 x

求解步骤

\frac{\partial}{\partial x} (x^{3} y + 12 x^{2} - 64 y)

将

y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{3} y) + \frac{\partial}{\partial x} (12 x^{2}) - \frac{\partial}{\partial x} (64 y)

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

\frac{\partial}{\partial x} (12 x^{2}) = 24 x

\frac{\partial}{\partial x} (64 y) = 0

= 3 y x^{2} + 24 x - 0

化简

= 3 x^{2} y + 24 x

\int (3 + 3 tan^{2} (x)) d x

d er i v a t i v e \frac{5 x ^{3}}{( 5 - 3 x ) ^{4}}

d er i v a t i v e f (x) = 5 (x^{3} - x)^{4}

\frac{d}{d x} (\frac{( x - 2 )}{x - 1})

d er i v a t i v e h (x) = (x + 1)^{7} - 7 x - 3