derivative f(x)=9xe^x

解答

导数

f (x) = 9 x e^{x}

9 (e^{x} + e^{x} x)

求解步骤

\frac{d}{d x} (9 x e^{x})

将常数提出:

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

= 9 \frac{d}{d x} (x e^{x})

使用微分乘法定则:

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

f = x, g = e^{x}

= 9 (\frac{d x}{d x} e^{x} + \frac{d}{d x} (e^{x}) x)

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

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

= 9 (1 \cdot e^{x} + e^{x} x)

化简

= 9 (e^{x} + e^{x} x)

\int \frac{m ^{3}}{( m ^{2} + 1 ) ^{3}} d m

x \to 2 lim (7 - 3 x^{2} - x^{3})

\frac{d}{d x} (\frac{1}{4} e^{2 x^{2}})

y^{^{''}} - 4 y^{^{'}} + 2 y = 0

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