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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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