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Popular >

derivative of sqrt(ln(x+x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of-2x+y

\frac{d}{d x} (- 2 x + y)

integral of u+1

\int u + 1 d u

y=sec(1+\sqrt[3]{4+arcsin(4+pi^2)})

y = sec (1 + 3 4 + arcsin (4 + π^{2}))

10(t+1)(dy)/(dt)-9y=9t

10 (t + 1) \frac{d y}{d t} - 9 y = 9 t

limit as x approaches 0 of (-cos(x)+1)/x

x \to 0 lim (\frac{- cos ( x ) + 1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(ln(x+x)) ?
The derivative of sqrt(ln(x+x)) is (1+x)/(2xsqrt(ln(x)+x))
What is the first derivative of sqrt(ln(x+x)) ?
The first derivative of sqrt(ln(x+x)) is (1+x)/(2xsqrt(ln(x)+x))