derivative of 2x*sin(x)

解答

\frac{d}{d x} (2 x \cdot sin (x))

2 (sin (x) + x cos (x))

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = sin (x)

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot sin (x) + cos (x) x)

化简

= 2 (sin (x) + x cos (x))