derivative 7x^3e^x

解答

导数

7 x^{3} e^{x}

7 (3 x^{2} e^{x} + e^{x} x^{3})

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x^{3}, g = e^{x}

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

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

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

= 7 (3 x^{2} e^{x} + e^{x} x^{3})

t an g e n t f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 4

\int \frac{x ^{3} + 3 x - 1}{x ^{4} - 4 x ^{2}} d x

\frac{d}{d x} ((1 + 8 x^{2}) (x - x^{2}))

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

\frac{d}{d x} (3 sin (5 x))