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

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

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

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

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derivative of

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

3 e^{3 e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{3 e^{x}} \cdot 3 e^{x}

Apply exponent rule:

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

e^{3 e^{x}} e^{x} = e^{3 e^{x} + x}

= 3 e^{3 e^{x} + x}

(5.4) 8 x^{2} - 9 y^{3} = - 376

f (x) = 7 x^{4} + 13 x^{3} - 22 x^{2} + 5 x - 3

x (\frac{d y}{d x}) = - y + 2 x^{2} y

\int y \cdot e^{y} d y

\int x sin (b x) d x

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