derivative x^3sin(7x)

解答

导数

x^{3} sin (7 x)

3 x^{2} sin (7 x) + cos (7 x) \cdot 7 x^{3}

求解步骤

\frac{d}{d x} (x^{3} sin (7 x))

使用微分乘法定则:

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

f = x^{3}, g = sin (7 x)

= \frac{d}{d x} (x^{3}) sin (7 x) + \frac{d}{d x} (sin (7 x)) x^{3}

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

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= 3 x^{2} sin (7 x) + cos (7 x) \cdot 7 x^{3}

\frac{d}{d x} (6 + 7 x)

t a y l or e^{3 x}, 0

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

\frac{\partial}{\partial h} (\frac{1}{2} (a + b) h)

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