What is (\partial)/(\partial x)(ln(x^3+y^2)) ?

The answer to (\partial)/(\partial x)(ln(x^3+y^2)) is (3x^2)/(x^3+y^2)

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(\partial)/(\partial x)(ln(x^3+y^2))

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}))

\frac{3 x ^{2}}{x ^{3} + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}))

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{3} + y^{2}) = 3 x^{2}

= \frac{1}{x ^{3} + y ^{2}} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + y ^{2}} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + y ^{2}}

= \frac{3 x ^{2}}{x ^{3} + y ^{2}}

\frac{d}{d x} (sec (\frac{x}{2}))

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What is (\partial)/(\partial x)(ln(x^3+y^2)) ?
The answer to (\partial)/(\partial x)(ln(x^3+y^2)) is (3x^2)/(x^3+y^2)