What is the derivative of y=ln(ln(sqrt(x))) ?

The derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))

What is the first derivative of y=ln(ln(sqrt(x))) ?

The first derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))

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derivative of

y = ln (ln (x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{- l n (4)}^{0} 3 e^{t} d t

f (x) = x^{3} - 1.5 x^{2} - 90 x - 22

- 5 + 3 x^{2}

\int_{0}^{1} 3 e^{- 7 x} d x

\int - 4 + tan^{2} (x) d x

What is the derivative of y=ln(ln(sqrt(x))) ?
The derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))
What is the first derivative of y=ln(ln(sqrt(x))) ?
The first derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))