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

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

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

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

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\frac{d}{d 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}

\int \frac{2}{3} x^{\frac{3}{2}} - 6 sin (x) + C d x

y^{^{'}} = x^{2} - 1, y (0) = 1

\int \frac{1}{289 + x ^{2}} d x

\int_{0}^{1} (x^{15} + 1 5^{x}) d x

x^{2} y^{^{''}} - x y^{^{'}} + y = x

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