derivative of xsqrt(5-x)

解答

\frac{d}{d x} (x 5 - x)

\frac{- 3 x + 10}{2 5 - x}

求解步骤

\frac{d}{d x} (x 5 - x)

使用微分乘法定则:

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

f = x, g = 5 - x

= \frac{d x}{d x} 5 - x + \frac{d}{d x} (5 - x) x

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

\frac{d}{d x} (5 - x) = - \frac{1}{2 5 - x}

= 1 \cdot 5 - x + (- \frac{1}{2 5 - x}) x

化简

1 \cdot 5 - x + (- \frac{1}{2 5 - x}) x : \frac{- 3 x + 10}{2 5 - x}

= \frac{- 3 x + 10}{2 5 - x}

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