(\partial)/(\partial x)(5x^2+y+sin(axy)+3)

解答

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

a y cos (a x y) + 10 x

求解步骤

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

将

a, y

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (sin (a x y)) + \frac{\partial}{\partial x} (3)

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

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

\frac{\partial}{\partial x} (3) = 0

= 10 x + 0 + cos (a x y) a y + 0

化简

= a y cos (a x y) + 10 x

\int \frac{3 x ( 8 - x )}{135} d x

d er i v a t i v e y = 2^{x} ln (5)

\int \frac{x}{y} + \frac{y}{x} d y

\int_{0}^{2} x^{3} 1 + 9 x^{4} d x

\frac{d}{d x} (8 arctan (x))