What is (\partial)/(\partial x)(ln(9x^2+5y^2)) ?

The answer to (\partial)/(\partial x)(ln(9x^2+5y^2)) is (18x)/(9x^2+5y^2)

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(\partial)/(\partial x)(ln(9x^2+5y^2))

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

\frac{18 x}{9 x ^{2} + 5 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (ln (9 x^{2} + 5 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{9 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 5 y^{2})

= \frac{1}{9 x ^{2} + 5 y ^{2}} \frac{\partial}{\partial x} (9 x^{2} + 5 y^{2})

\frac{\partial}{\partial x} (9 x^{2} + 5 y^{2}) = 18 x

= \frac{1}{9 x ^{2} + 5 y ^{2}} \cdot 18 x

Simplify

\frac{1}{9 x ^{2} + 5 y ^{2}} \cdot 18 x : \frac{18 x}{9 x ^{2} + 5 y ^{2}}

= \frac{18 x}{9 x ^{2} + 5 y ^{2}}

What is (\partial)/(\partial x)(ln(9x^2+5y^2)) ?
The answer to (\partial)/(\partial x)(ln(9x^2+5y^2)) is (18x)/(9x^2+5y^2)