derivative of x*sin(3x)

解答

\frac{d}{d x} (x \cdot sin (3 x))

sin (3 x) + 3 x cos (3 x)

求解步骤

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

使用微分乘法定则:

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

f = x, g = sin (3 x)

= \frac{d x}{d x} sin (3 x) + \frac{d}{d x} (sin (3 x)) x

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 1 \cdot sin (3 x) + cos (3 x) \cdot 3 x

化简

= sin (3 x) + 3 x cos (3 x)

\frac{d}{d x} (x^{4} + 4)

\frac{d}{d x} (x - y + 1)

\frac{\partial}{\partial y} (4 y^{2})

\frac{d}{d x} (ln (5 x^{2}))

s l o p e (x^{2} + y^{2})^{2} = 4 x^{2} y