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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to \infty lim (1 - x^{2})

\frac{1}{2 - x} + \frac{1}{2 - 3 x}

\int \frac{7 x ^{2} - 6 x + 16}{x ^{3} + 4 x} d x

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 80 cos (8 t)

x \to - 3 lim (x + 3)

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