What is (\partial)/(\partial x)(ln((y^9)/(x^7))) ?

The answer to (\partial)/(\partial x)(ln((y^9)/(x^7))) is -7/x

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(\partial)/(\partial x)(ln((y^9)/(x^7)))

\frac{\partial}{\partial x} (ln (\frac{y ^{9}}{x ^{7}}))

- \frac{7}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{y ^{9}}{x ^{7}}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{\frac{y ^{9}}{x ^{7}}} \frac{\partial}{\partial x} (\frac{y ^{9}}{x ^{7}})

= \frac{1}{\frac{y ^{9}}{x ^{7}}} \frac{\partial}{\partial x} (\frac{y ^{9}}{x ^{7}})

\frac{\partial}{\partial x} (\frac{y ^{9}}{x ^{7}}) = - \frac{7 y ^{9}}{x ^{8}}

= \frac{1}{\frac{y ^{9}}{x ^{7}}} (- \frac{7 y ^{9}}{x ^{8}})

Simplify

\frac{1}{\frac{y ^{9}}{x ^{7}}} (- \frac{7 y ^{9}}{x ^{8}}) : - \frac{7}{x}

= - \frac{7}{x}

x \to 0 lim (+ (\frac{ln ( x )}{x}))

\frac{\partial}{\partial x} (x e^{- x})

\int (9 - y) y d y

n = 1 \sum \infty (cos (24))^{n}

x \to 0 lim (\frac{x ^{2}}{2} - \frac{2}{x})

What is (\partial)/(\partial x)(ln((y^9)/(x^7))) ?
The answer to (\partial)/(\partial x)(ln((y^9)/(x^7))) is -7/x