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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int 4 x cos (5 x) d x

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x + 5, at x = 1

\int \frac{3}{1 - 4 x} d x

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