What is the derivative of e^{ln(ln(2x)}) ?

The derivative of e^{ln(ln(2x)}) is 1/x

What is the first derivative of e^{ln(ln(2x)}) ?

The first derivative of e^{ln(ln(2x)}) is 1/x

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

\frac{1}{x}

Solution steps

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

Simplify

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

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

Apply the chain rule:

\frac{1}{2 x} \frac{d}{d x} (2 x)

= \frac{1}{2 x} \frac{d}{d x} (2 x)

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

= \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{2 x} \cdot 2 : \frac{1}{x}

= \frac{1}{x}

What is the derivative of e^{ln(ln(2x)}) ?
The derivative of e^{ln(ln(2x)}) is 1/x
What is the first derivative of e^{ln(ln(2x)}) ?
The first derivative of e^{ln(ln(2x)}) is 1/x