derivative of sqrt(sin(\sqrt{1+x^2)})

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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