What is the derivative of e^{9e^x} ?

The derivative of e^{9e^x} is 9e^{9e^x+x}

What is the first derivative of e^{9e^x} ?

The first derivative of e^{9e^x} is 9e^{9e^x+x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

e^{9 e^{x}}

9 e^{9 e^{x} + x}

Solution steps

\frac{d}{d x} (e^{9 e^{x}})

Apply the chain rule:

e^{9 e^{x}} \frac{d}{d x} (9 e^{x})

= e^{9 e^{x}} \frac{d}{d x} (9 e^{x})

\frac{d}{d x} (9 e^{x}) = 9 e^{x}

= e^{9 e^{x}} \cdot 9 e^{x}

Apply exponent rule:

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

e^{9 e^{x}} e^{x} = e^{9 e^{x} + x}

= 9 e^{9 e^{x} + x}

\frac{d y}{d x} = \frac{1}{6 x - 42}

y = \frac{e ^{4 x^{2} + 1}}{8}

2 x + 5 x

h (x) = x^{2}

f (x) = \frac{1}{x ^{2} + 3}

What is the derivative of e^{9e^x} ?
The derivative of e^{9e^x} is 9e^{9e^x+x}
What is the first derivative of e^{9e^x} ?
The first derivative of e^{9e^x} is 9e^{9e^x+x}