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Popular >

derivative of ln(sqrt(3x))

Solution

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

Solution

\frac{1}{2 x}

Solution steps

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

Simplify

ln (3 x) : ln (3 x)

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

Apply the chain rule:

\frac{1}{3 x} \frac{d}{d x} (3 x)

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

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= \frac{1}{3 x} \cdot \frac{3}{2 x}

Simplify

\frac{1}{3 x} \cdot \frac{3}{2 x} : \frac{1}{2 x}

= \frac{1}{2 x}

Popular Examples

integral from-1 to 0 of 6/(1+(2x+1)^2)

\int_{- 1}^{0} \frac{6}{1 + ( 2 x + 1 ) ^{2}} d x

(\partial)/(\partial y)(ye^{xy}+sin(y))

\frac{\partial}{\partial y} (y e^{x y} + sin (y))

integral of e^{ax}sin(bx)

\int e^{a x} sin (b x) d x

(\partial)/(\partial x)(e^{-x}sin(y)z)

\frac{\partial}{\partial x} (e^{- x} sin (y) z)

sum from n=1 to infinity of (3n)/(6n+13)

n = 1 \sum \infty \frac{3 n}{6 n + 13}

Frequently Asked Questions (FAQ)

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