(d^{10})/(dx^{10)}(cos(2x))

解

\frac{d ^{10}}{d x ^{10}} (cos (2 x))

- 1024 cos (2 x)

解答ステップ

\frac{d ^{10}}{d x ^{10}} (cos (2 x))

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

= \frac{d ^{9}}{d x ^{9}} (- sin (2 x) \cdot 2)

\frac{d}{d x} (- sin (2 x) \cdot 2) = - 4 cos (2 x)

= \frac{d ^{8}}{d x ^{8}} (- 4 cos (2 x))

\frac{d}{d x} (- 4 cos (2 x)) = 8 sin (2 x)

= \frac{d ^{7}}{d x ^{7}} (8 sin (2 x))

\frac{d}{d x} (8 sin (2 x)) = 16 cos (2 x)

= \frac{d ^{6}}{d x ^{6}} (16 cos (2 x))

\frac{d}{d x} (16 cos (2 x)) = - 32 sin (2 x)

= \frac{d ^{5}}{d x ^{5}} (- 32 sin (2 x))

\frac{d}{d x} (- 32 sin (2 x)) = - 64 cos (2 x)

= \frac{d ^{4}}{d x ^{4}} (- 64 cos (2 x))

\frac{d}{d x} (- 64 cos (2 x)) = 128 sin (2 x)

= \frac{d ^{3}}{d x ^{3}} (128 sin (2 x))

\frac{d}{d x} (128 sin (2 x)) = 256 cos (2 x)

= \frac{d ^{2}}{d x ^{2}} (256 cos (2 x))

\frac{d}{d x} (256 cos (2 x)) = - 512 sin (2 x)

= \frac{d}{d x} (- 512 sin (2 x))

\frac{d}{d x} (- 512 sin (2 x)) = - 1024 cos (2 x)

= - 1024 cos (2 x)