derivative f(x)=sin(x^2)+(1-x)/(1+x)

解

導関数

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

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

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

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

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