derivative-1/4 cos^4(x)

解答

导数

- \frac{1}{4} cos^{4} (x)

cos^{3} (x) sin (x)

求解步骤

\frac{d}{d x} (- \frac{1}{4} cos^{4} (x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{4} \frac{d}{d x} (cos^{4} (x))

使用连锁律:

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

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

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

= - \frac{1}{4} \cdot 4 (cos (x))^{3} (- sin (x))

化简

- \frac{1}{4} \cdot 4 cos^{3} (x) (- sin (x)) : cos^{3} (x) sin (x)

= cos^{3} (x) sin (x)

\int e^{- 4 x} sin (3 x) d x

\int \frac{x ^{3}}{3 1 - x ^{2}} d x

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

\int \frac{7}{( z - 10 ) ^{7}} d z

\frac{d}{d x} ((2 x + 5)^{3})