derivative d(x)(55)/(0.01x^2+1)

解

導関数

d (x) \frac{55}{0.01 x ^{2} + 1}

\frac{55 d ( - 0.01 x ^{2} + 1 )}{( 0.01 x ^{2} + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (d x \frac{55}{0.01 x ^{2} + 1})

定数を除去:

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

= d \cdot 55 \frac{d}{d x} (x \frac{1}{0.01 x ^{2} + 1})

積の法則を適用:

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

f = x, g = \frac{1}{0.01 x ^{2} + 1}

= d \cdot 55 (\frac{d x}{d x} \frac{1}{0.01 x ^{2} + 1} + \frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1}) x)

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

\frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1}) = - \frac{0.02 x}{( 0.01 x ^{2} + 1 ) ^{2}}

= d \cdot 55 (1 \cdot \frac{1}{0.01 x ^{2} + 1} + (- \frac{0.02 x}{( 0.01 x ^{2} + 1 ) ^{2}}) x)

簡素化

d \cdot 55 (1 \cdot \frac{1}{0.01 x ^{2} + 1} + (- \frac{0.02 x}{( 0.01 x ^{2} + 1 ) ^{2}}) x) : \frac{55 d ( - 0.01 x ^{2} + 1 )}{( 0.01 x ^{2} + 1 ) ^{2}}

= \frac{55 d ( - 0.01 x ^{2} + 1 )}{( 0.01 x ^{2} + 1 ) ^{2}}