What is the derivative of e^xx ?

The derivative of e^xx is e^xx+e^x

What is the first derivative of e^xx ?

The first derivative of e^xx is e^xx+e^x

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derivative of

e^{x} x

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

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

\frac{d x}{d x} = 1

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

Simplify

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

\int e^{7 x} cos (9 x) d x

t^{2} + t + 1

x \to 0 lim (\frac{cos ( 2 x ) - 1}{x})

\int \frac{25}{x} d x

\int 16 t + sec^{2} (t) d t