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

The derivative of (x^2+1e^x) is 2xe^x+e^x(x^2+1)

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

The first derivative of (x^2+1e^x) is 2xe^x+e^x(x^2+1)

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

2 x e^{x} + e^{x} (x^{2} + 1)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

What is the derivative of (x^2+1e^x) ?
The derivative of (x^2+1e^x) is 2xe^x+e^x(x^2+1)
What is the first derivative of (x^2+1e^x) ?
The first derivative of (x^2+1e^x) is 2xe^x+e^x(x^2+1)