derivative of 8cos^3(x)

解答

\frac{d}{d x} (8 cos^{3} (x))

- 24 cos^{2} (x) sin (x)

求解步骤

\frac{d}{d x} (8 cos^{3} (x))

将常数提出:

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

= 8 \frac{d}{d x} (cos^{3} (x))

使用连锁律:

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

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

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

= 8 \cdot 3 (cos (x))^{2} (- sin (x))

化简

= - 24 cos^{2} (x) sin (x)

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

y^{^{''}} + a = 0

f^{^{'}} (x) = x^{4}

s

\frac{\partial}{\partial y} (x e^{6 y})