What is (\partial)/(\partial x)(ln(x/4+y/(12))) ?

The answer to (\partial)/(\partial x)(ln(x/4+y/(12))) is 3/(3x+y)

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(\partial)/(\partial x)(ln(x/4+y/(12)))

\frac{\partial}{\partial x} (ln (\frac{x}{4} + \frac{y}{12}))

\frac{3}{3 x + y}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{4} + \frac{y}{12}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{\frac{x}{4} + \frac{y}{12}} \frac{\partial}{\partial x} (\frac{x}{4} + \frac{y}{12})

= \frac{1}{\frac{x}{4} + \frac{y}{12}} \frac{\partial}{\partial x} (\frac{x}{4} + \frac{y}{12})

\frac{\partial}{\partial x} (\frac{x}{4} + \frac{y}{12}) = \frac{1}{4}

= \frac{1}{\frac{x}{4} + \frac{y}{12}} \cdot \frac{1}{4}

Simplify

\frac{1}{\frac{x}{4} + \frac{y}{12}} \cdot \frac{1}{4} : \frac{3}{3 x + y}

= \frac{3}{3 x + y}

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What is (\partial)/(\partial x)(ln(x/4+y/(12))) ?
The answer to (\partial)/(\partial x)(ln(x/4+y/(12))) is 3/(3x+y)