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Popular >

derivative of ln(ln(x^{2x}))

Solution

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

Solution

\frac{ln ( x ) + 1}{x ln ( x )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x^{2 x})) = 2 (ln (x) + 1)

= \frac{1}{ln ( x ^{2 x} )} \cdot 2 (ln (x) + 1)

Simplify

\frac{1}{ln ( x ^{2 x} )} \cdot 2 (ln (x) + 1) : \frac{ln ( x ) + 1}{x ln ( x )}

= \frac{ln ( x ) + 1}{x ln ( x )}

Graph

Popular Examples

integral of (27)/(x(x^2+4)^2)

\int \frac{27}{x ( x ^{2} + 4 ) ^{2}} d x

(dy)/(dx)=ln(x^y)

\frac{d y}{d x} = ln (x^{y})

integral of (x^4-4^x+\sqrt[4]{x}-4/x)

\int (x^{4} - 4^{x} + 4 x - \frac{4}{x}) d x

derivative of y=((x+7))/((x-5))derivative of

y = \frac{( x + 7 )}{( x - 5 )}

derivative of 1/2*ln(x)

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

Frequently Asked Questions (FAQ)

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