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

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

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

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

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

e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= e^{x} x^{2}

\int 15 x + \frac{3}{x} d x

y = x^{2} + 2 x + 1

x \frac{d y}{d x} = y^{2} + 1

\int (\frac{1}{4 + x ^{2}}) d x

(\frac{x ^{2}}{x ^{2} - x - 2})^{^{'}}

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