(d^3)/(dx^3)(e^xcos(x))

解

\frac{d ^{3}}{d x ^{3}} (e^{x} cos (x))

- 2 (e^{x} sin (x) + cos (x) e^{x})

解答ステップ

\frac{d ^{3}}{d x ^{3}} (e^{x} cos (x))

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

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

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

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

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

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