derivative of-3cos^2(xsin(x))

解答

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

- 3 (- 2 cos (x) + 3 cos^{3} (x))

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos^{2} (x), g = sin (x)

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

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

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

= - 3 ((- sin (2 x)) sin (x) + cos (x) cos^{2} (x))

化简

- 3 ((- sin (2 x)) sin (x) + cos (x) cos^{2} (x)) : - 3 (- 2 cos (x) + 3 cos^{3} (x))

= - 3 (- 2 cos (x) + 3 cos^{3} (x))

\int \frac{1}{x ( x ^{2} - 9 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = 2 (y^{2} + 1)

\frac{d y}{d x} + e^{x} y = x^{2} y^{2}

x \to - 2 lim (3 x^{3} - 4 x + 2)

\int \frac{2}{( x ^{2} + 1 ) ^{2} x ^{2}} d x