What is the derivative of f(x)=(x^2+3x-1)e^x ?

The derivative of f(x)=(x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x

What is the first derivative of f(x)=(x^2+3x-1)e^x ?

The first derivative of f(x)=(x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x

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derivative of

f (x) = (x^{2} + 3 x - 1) e^{x}

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

Solution steps

\frac{d}{d x} ((x^{2} + 3 x - 1) e^{x})

Apply the Product Rule:

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

f = x^{2} + 3 x - 1, g = e^{x}

= \frac{d}{d x} (x^{2} + 3 x - 1) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} + 3 x - 1)

\frac{d}{d x} (x^{2} + 3 x - 1) = 2 x + 3

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

= (2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 1)

Simplify

(2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 1) : e^{x} x^{2} + 5 e^{x} x + 2 e^{x}

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

What is the derivative of f(x)=(x^2+3x-1)e^x ?
The derivative of f(x)=(x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x
What is the first derivative of f(x)=(x^2+3x-1)e^x ?
The first derivative of f(x)=(x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x