(d^3)/(dx^3)(x^2sin(sqrt(x)))

解

\frac{d ^{3}}{d x ^{3}} (x^{2} sin (x))

\frac{- x cos ( x ) - 9 x sin ( x ) + 15 cos ( x )}{8 x}

解答ステップ

\frac{d ^{3}}{d x ^{3}} (x^{2} sin (x))

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

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

\frac{d}{d x} (2 x sin (x) + \frac{x ^{\frac{3}{2}} cos ( x )}{2}) = \frac{- x sin ( x ) + 7 x cos ( x ) + 8 sin ( x )}{4}

= \frac{d}{d x} (\frac{- x sin ( x ) + 7 x cos ( x ) + 8 sin ( x )}{4})

\frac{d}{d x} (\frac{- x sin ( x ) + 7 x cos ( x ) + 8 sin ( x )}{4}) = \frac{- x cos ( x ) - 9 x sin ( x ) + 15 cos ( x )}{8 x}

= \frac{- x cos ( x ) - 9 x sin ( x ) + 15 cos ( x )}{8 x}