(\partial)/(\partial x)(1/4 (x+y)^4)

解答

\frac{\partial}{\partial x} (\frac{1}{4} (x + y)^{4})

(x + y)^{3}

求解步骤

\frac{\partial}{\partial x} (\frac{1}{4} (x + y)^{4})

将

y

视为常数

将常数提出:

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

= \frac{1}{4} \frac{\partial}{\partial x} ((x + y)^{4})

使用连锁律:

4 (x + y)^{3} \frac{\partial}{\partial x} (x + y)

= 4 (x + y)^{3} \frac{\partial}{\partial x} (x + y)

\frac{\partial}{\partial x} (x + y) = 1

= \frac{1}{4} \cdot 4 (x + y)^{3} \cdot 1

化简

\frac{1}{4} \cdot 4 (x + y)^{3} \cdot 1 : (x + y)^{3}

= (x + y)^{3}

- 4 x + \frac{2 x d y}{d x} = \frac{2 d y}{d x} + 3 x^{2} + 2

t an g e n t y = \frac{1}{( 1 + x ^{2} ) , at ( 1 , \frac{1}{2} )}

\int_{0}^{1} 1 + 7 x d x

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

d er i v a t i v e 4 x^{- 2}