derivative f(x)=sqrt((x^2)sin(x-2))

解

導関数

f (x) = (x^{2}) sin (x - 2)

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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