derivative f(x)=8sin^4(sqrt(x))

解答

导数

f (x) = 8 sin^{4} (x)

\frac{16 sin ^{3} ( x ) cos ( x )}{x}

求解步骤

\frac{d}{d x} (8 sin^{4} (x))

将常数提出:

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

= 8 \frac{d}{d x} (sin^{4} (x))

使用连锁律:

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

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

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

= 8 \cdot 4 (sin (x))^{3} \frac{cos ( x )}{2 x}

化简

8 \cdot 4 sin^{3} (x) \frac{cos ( x )}{2 x} : \frac{16 sin ^{3} ( x ) cos ( x )}{x}

= \frac{16 sin ^{3} ( x ) cos ( x )}{x}

\frac{d}{d x} (6 x^{5} - 15 x^{4} + 10 x^{3})

\frac{\partial}{\partial x} (\frac{x}{y + 5 z})

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

t a y l or (- 3 x + 28)^{\frac{5}{4}}

\int_{0}^{7} \frac{1}{49 + x ^{2}} d x