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Popular >

derivative of sqrt(x+ln(3x))

Solution

\frac{d}{d x} (x + ln (3 x))

Solution

\frac{x + 1}{2 x x + ln ( 3 x )}

Solution steps

\frac{d}{d x} (x + ln (3 x))

Apply the chain rule:

\frac{1}{2 x + ln ( 3 x )} \frac{d}{d x} (x + ln (3 x))

= \frac{1}{2 x + ln ( 3 x )} \frac{d}{d x} (x + ln (3 x))

\frac{d}{d x} (x + ln (3 x)) = 1 + \frac{1}{x}

= \frac{1}{2 x + ln ( 3 x )} (1 + \frac{1}{x})

Simplify

\frac{1}{2 x + ln ( 3 x )} (1 + \frac{1}{x}) : \frac{x + 1}{2 x x + ln ( 3 x )}

= \frac{x + 1}{2 x x + ln ( 3 x )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x+ln(3x)) ?
The derivative of sqrt(x+ln(3x)) is (x+1)/(2xsqrt(x+ln(3x)))
What is the first derivative of sqrt(x+ln(3x)) ?
The first derivative of sqrt(x+ln(3x)) is (x+1)/(2xsqrt(x+ln(3x)))