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人気のある微分積分 >

derivative xsqrt(a+bx)

解

導関数

x a + b x

解

\frac{3 b x + 2 a}{2 a + b x}

解答ステップ

\frac{d}{d x} (x a + b x)

積の法則を適用:

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

f = x, g = a + b x

= \frac{d x}{d x} a + b x + \frac{d}{d x} (a + b x) x

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

\frac{d}{d x} (a + b x) = \frac{b}{2 a + b x}

= 1 \cdot a + b x + \frac{b}{2 a + b x} x

簡素化

1 \cdot a + b x + \frac{b}{2 a + b x} x : \frac{3 b x + 2 a}{2 a + b x}

= \frac{3 b x + 2 a}{2 a + b x}

グラフ

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