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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - \frac{1}{x} + C d x

2 x y \frac{d y}{d x} = y^{2} - x^{2}

\int (3 x^{2} + 2 e^{x}) d x

x \to 0 + lim (\frac{∣ x sin ( x ) ∣}{x})

\frac{d}{d x} (sin (e^{5 x}))

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