What is the derivative of f(x)=2^{2^x} ?

The derivative of f(x)=2^{2^x} is ln^2(2)*2^{2^x+x}

What is the first derivative of f(x)=2^{2^x} ?

The first derivative of f(x)=2^{2^x} is ln^2(2)*2^{2^x+x}

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derivative of

f (x) = 2^{2^{x}}

ln^{2} (2) \cdot 2^{2^{x} + x}

Solution steps

\frac{d}{d x} (2^{2^{x}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{2^{x}} = e^{2^{x} l n (2)}

= \frac{d}{d x} (e^{2^{x} l n (2)})

Apply the chain rule:

e^{2^{x} l n (2)} \frac{d}{d x} (2^{x} ln (2))

= e^{2^{x} l n (2)} \frac{d}{d x} (2^{x} ln (2))

\frac{d}{d x} (2^{x} ln (2)) = ln^{2} (2) \cdot 2^{x}

= e^{2^{x} l n (2)} ln^{2} (2) \cdot 2^{x}

Simplify

e^{2^{x} l n (2)} ln^{2} (2) \cdot 2^{x} : ln^{2} (2) \cdot 2^{2^{x} + x}

= ln^{2} (2) \cdot 2^{2^{x} + x}

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What is the derivative of f(x)=2^{2^x} ?
The derivative of f(x)=2^{2^x} is ln^2(2)*2^{2^x+x}
What is the first derivative of f(x)=2^{2^x} ?
The first derivative of f(x)=2^{2^x} is ln^2(2)*2^{2^x+x}