derivative f(x)=8sin^6(sqrt(x))

解答

导数

f (x) = 8 sin^{6} (x)

\frac{24 sin ^{5} ( x ) cos ( x )}{x}

求解步骤

\frac{d}{d x} (8 sin^{6} (x))

将常数提出:

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

= 8 \frac{d}{d x} (sin^{6} (x))

使用连锁律:

6 (sin (x))^{5} \frac{d}{d x} (sin (x))

= 6 (sin (x))^{5} \frac{d}{d x} (sin (x))

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

= 8 \cdot 6 (sin (x))^{5} \frac{cos ( x )}{2 x}

化简

8 \cdot 6 sin^{5} (x) \frac{cos ( x )}{2 x} : \frac{24 sin ^{5} ( x ) cos ( x )}{x}

= \frac{24 sin ^{5} ( x ) cos ( x )}{x}

x \to 4 + lim (\frac{1}{∣ 4 - x ∣})

s l o p e y = x^{3}, at x = 5

\frac{d}{d x} (3 x^{4} - 2 x^{3} - 12 x^{2} + 18 x + 15)

\frac{d}{d x} (\frac{1}{ln ( x ^{2} )})

\frac{\partial}{\partial y} (ln (x^{2} y^{2}))