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}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\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}

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

d er i v a t i v e f (x) = 5 (9 x^{7} + 3 x^{4} - 2)^{3}

x \to 0 + lim (x^{\frac{4}{x}})

\int \frac{x ^{4} + 5 x - 3}{x ^{2}} d x

\frac{d}{d x} ((3 x^{6} - 2 x^{4})^{4})

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}