What is (\partial)/(\partial p)(ln((p+q)/(q^2))) ?

The answer to (\partial)/(\partial p)(ln((p+q)/(q^2))) is 1/(p+q)

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(\partial)/(\partial p)(ln((p+q)/(q^2)))

\frac{\partial}{\partial p} (ln (\frac{p + q}{q ^{2}}))

\frac{1}{p + q}

Solution steps

\frac{\partial}{\partial p} (ln (\frac{p + q}{q ^{2}}))

Treat

q

as a constant

Apply the chain rule:

\frac{1}{\frac{p + q}{q ^{2}}} \frac{\partial}{\partial p} (\frac{p + q}{q ^{2}})

= \frac{1}{\frac{p + q}{q ^{2}}} \frac{\partial}{\partial p} (\frac{p + q}{q ^{2}})

\frac{\partial}{\partial p} (\frac{p + q}{q ^{2}}) = \frac{1}{q ^{2}}

= \frac{1}{\frac{p + q}{q ^{2}}} \cdot \frac{1}{q ^{2}}

Simplify

\frac{1}{\frac{p + q}{q ^{2}}} \cdot \frac{1}{q ^{2}} : \frac{1}{p + q}

= \frac{1}{p + q}

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

n = 0 \sum \infty \frac{5}{e ^{2 n}}

\frac{d}{d x} (e^{x - 1} - 1)

\frac{d y}{d x} = x^{8} y

f (x) = 1 (- 5 x + 3) (- 3 x + 2)

What is (\partial)/(\partial p)(ln((p+q)/(q^2))) ?
The answer to (\partial)/(\partial p)(ln((p+q)/(q^2))) is 1/(p+q)