derivative 2sin^4(sqrt(x))

解答

导数

2 sin^{4} (x)

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

求解步骤

\frac{d}{d x} (2 sin^{4} (x))

将常数提出:

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

= 2 \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}

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

化简

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

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

\int \frac{1}{( 2 - y ) ( 1 - y )} d y

\frac{\partial}{\partial x} (2 ln (x) + 5 ln (y))

\int (5 x^{3} + 6 x) e^{x^{2}} d x

\int \frac{1}{9 y ^{2} + 4} d y

\int (1 - x) d x