derivative of (x^2+3x-9e^x)

解答

\frac{d}{d x} ((x^{2} + 3 x - 9) e^{x})

e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

求解步骤

\frac{d}{d x} ((x^{2} + 3 x - 9) e^{x})

使用微分乘法定则:

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

f = x^{2} + 3 x - 9, g = e^{x}

= \frac{d}{d x} (x^{2} + 3 x - 9) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} + 3 x - 9)

\frac{d}{d x} (x^{2} + 3 x - 9) = 2 x + 3

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

= (2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 9)

化简

(2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 9) : e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

= e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

\frac{d}{d x} (x^{3} + k y (x)^{2} - 5 x y)

t an g e n t \frac{16 x}{x ^{2} + 16}, at - 2, - \frac{8}{5}

\frac{\partial}{\partial x} (2 e^{x y})

\int \frac{2 - x ^{2}}{x} d x

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