derivative of 3xy^3

解答

\frac{d}{d x} (3 x y^{3})

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

求解步骤

\frac{d}{d x} (3 x y^{3})

将常数提出:

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

= 3 \frac{d}{d x} (x y^{3})

使用微分乘法定则:

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

f = x, g = y^{3}

= 3 (\frac{d x}{d x} y^{3} + \frac{d}{d x} (y^{3}) x)

\frac{d x}{d x} = 1

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

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

化简

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

y^{^{''}} = - 9 sin (5 x)

\frac{\partial}{\partial x} (\frac{2}{x} - n)

\int (8 t^{3} - 6 t^{- 2}) d t

x \to - 1^{- 1} lim (\frac{x}{x + 1})

\int \frac{9}{x + 9 + x} d x