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Popular >

derivative of xln(ln(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (ln (x))

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Graph

Popular Examples

integral of (x^2+1)/((x+2)(x^2+2x+5))

\int \frac{x ^{2} + 1}{( x + 2 ) ( x ^{2} + 2 x + 5 )} d x

implicit (dy)/(dx),2xy=5 implicit derivative

\frac{d y}{d x}, 2 x y = 5

y^'=(x^2e^{y/x}+y^2)/(xy)

y^{^{'}} = \frac{x ^{2} e ^{\frac{y}{x}} + y ^{2}}{x y}

derivative of (x-4(ln(x/4)))

\frac{d}{d x} ((x - 4) (ln (\frac{x}{4})))

derivative of f(x)=(e^x)/(7x^2+4)derivative of

f (x) = \frac{e ^{x}}{7 x ^{2} + 4}

Frequently Asked Questions (FAQ)

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