What is the derivative of (x^2+3x-9e^x) ?

The derivative of (x^2+3x-9e^x) is e^xx^2+5e^xx-6e^x

What is the first derivative of (x^2+3x-9e^x) ?

The first derivative of (x^2+3x-9e^x) is e^xx^2+5e^xx-6e^x

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

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

Solution steps

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

Apply the Product Rule:

(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)

Simplify

(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)

\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

x e^{x}, 0

What is the derivative of (x^2+3x-9e^x) ?
The derivative of (x^2+3x-9e^x) is e^xx^2+5e^xx-6e^x
What is the first derivative of (x^2+3x-9e^x) ?
The first derivative of (x^2+3x-9e^x) is e^xx^2+5e^xx-6e^x