What is (\partial)/(\partial x)(2ln(3x)) ?

The answer to (\partial)/(\partial x)(2ln(3x)) is 2/x

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(\partial)/(\partial x)(2ln(3x))

\frac{\partial}{\partial x} (2 ln (3 x))

\frac{2}{x}

Solution steps

\frac{\partial}{\partial x} (2 ln (3 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (ln (3 x))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 x) = 3

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

Simplify

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

= \frac{2}{x}

\frac{d}{d x} ((sin (x))^{x^{3}})

x \to 0 + lim (\frac{6 x}{sin ( x )})

f (x) = 8 x, (4, 16)

y = 3 x^{2}, y^{2} = \frac{1}{3} x

\int \frac{ln ^{2} ( x ^{2} )}{x} d x

What is (\partial)/(\partial x)(2ln(3x)) ?
The answer to (\partial)/(\partial x)(2ln(3x)) is 2/x