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

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

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

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

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derivative of

e^{x} (x + 1)

e^{x} x + 2 e^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= e^{x} (x + 1) + 1 \cdot e^{x}

Simplify

e^{x} (x + 1) + 1 \cdot e^{x} : e^{x} x + 2 e^{x}

= e^{x} x + 2 e^{x}

\int e^{- 5} d x

\int_{6}^{8} \frac{58}{( x - 6 ) ^{3}} d x

\frac{d}{d x} (x^{2} - y^{2})

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

x \to 2 lim (\frac{2 x - 5}{x + 7})

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