derivative f(x)=x^3e^3sin(x)

解答

导数

f (x) = x^{3} e^{3} sin (x)

e^{3} (3 x^{2} sin (x) + cos (x) x^{3})

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

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

x \to - 2 + lim (x + 11)

x \to 129 lim (\frac{( x - 129 )}{x + 15 - 12})

in v erse l a pl a ce \frac{5}{( s - 1 ) ^{3}}

\int x \frac{2}{3} d x

\frac{\partial}{\partial x} (x^{2} + x ln (yz))