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

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

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

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

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

e^{x} x^{2} - e^{x} x - e^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= e^{x} x^{2} - e^{x} x - e^{x}

\frac{d}{d θ} (sec (θ) \cdot tan (θ))

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

\int t^{2} sin (2 t) d t

f (x) = x^{\frac{1}{4}}

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