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Popular >

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

Solution

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

Solution

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (6x^5-7x/(x^4-8))

\frac{d}{d x} (\frac{6 x ^{5} - 7 x}{x ^{4} - 8})

integral of (6e^{-0.2x})

\int (6 e^{- 0.2 x}) d x

area 5-x,25-x^2 area

5 - x, 25 - x^{2}

integral of 1/(x^2)arctan(x)

\int \frac{1}{x ^{2}} arctan (x) d x

limit as x approaches 4+of sqrt(x-4)

x \to 4 + lim (x - 4)

Frequently Asked Questions (FAQ)

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