derivative of x/((x^2+1^{1/2)}-1)

解

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

\frac{1}{( x ^{2} + 1 ) ^{\frac{3}{2}}}

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} - 0

簡素化

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