derivative of 2xsin(2x)

解答

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

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

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = sin (2 x)

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

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

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

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

化简

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

y^{^{''}} + 2 y^{^{'}} + 10 y = cos (t) + 0.739

d er i v a t i v e f (x) = 11 x^{3} tan (x)

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})

\int \frac{1}{y ^{2} - y} d y

s l o p e f (x) = x^{2} + 2