What is the derivative derivative of e^{ex} ?

The derivative derivative of e^{ex} is e^{ex+1}

What is the first derivative derivative of e^{ex} ?

The first derivative derivative of e^{ex} is e^{ex+1}

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derivative

e^{e x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{e x} e

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

= e^{e x + 1}

What is the derivative derivative of e^{ex} ?
The derivative derivative of e^{ex} is e^{ex+1}
What is the first derivative derivative of e^{ex} ?
The first derivative derivative of e^{ex} is e^{ex+1}