What is the derivative of ee^x ?

The derivative of ee^x is e^{1+x}

What is the first derivative of ee^x ?

The first derivative of ee^x is e^{1+x}

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

e^{1 + x}

Solution steps

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

Simplify

e e^{x} : e^{1 + x}

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

Apply the chain rule:

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

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

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

= e^{1 + x} \cdot 1

Simplify

= e^{1 + x}