en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=3e^{3e^x+x}

Solution

derivative of

f (x) = 3 e^{3 e^{x} + x}

Solution

3 e^{3 e^{x} + x} (3 e^{x} + 1)

Solution steps

\frac{d}{d x} (3 e^{3 e^{x} + x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (e^{3 e^{x} + x})

Apply the chain rule:

e^{3 e^{x} + x} \frac{d}{d x} (3 e^{x} + x)

= e^{3 e^{x} + x} \frac{d}{d x} (3 e^{x} + x)

\frac{d}{d x} (3 e^{x} + x) = 3 e^{x} + 1

= 3 e^{3 e^{x} + x} (3 e^{x} + 1)

Popular Examples

(\partial)/(\partial x)(xz+e^{-x^2+y})

\frac{\partial}{\partial x} (x z + e^{- x^{2} + y})

derivative of 4^x+1

\frac{d}{d x} (4^{x} + 1)

derivative of x^2+3x+5

\frac{d}{d x} (x^{2} + 3 x + 5)

limit as x approaches 2 of 4/((x-2)^3)

x \to 2 lim (\frac{4}{( x - 2 ) ^{3}})

derivative of dcos(x+x^2sin(x))

\frac{d}{d x} (d cos (x) + x^{2} sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=3e^{3e^x+x} ?
The derivative of f(x)=3e^{3e^x+x} is 3e^{3e^x+x}(3e^x+1)
What is the first derivative of f(x)=3e^{3e^x+x} ?
The first derivative of f(x)=3e^{3e^x+x} is 3e^{3e^x+x}(3e^x+1)