What is the derivative of e^{ex} ?

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

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

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

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

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}

x \to + (- \infty) + lim (- 2)

\int \frac{4 - x}{16 - x ^{2}} d x

\frac{d}{d x} (r (h, t, x) i g (h, t, x) h t)

\int (x + 1)^{2} \cdot x^{2} d x

f (x) = 5 (9 x^{7} + 3 x^{4} - 2)^{3}

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