What is (\partial)/(\partial y)(ln(sqrt(3x)+5y)) ?

The answer to (\partial)/(\partial y)(ln(sqrt(3x)+5y)) is 5/(sqrt(3)\sqrt{x)+5y}

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(\partial)/(\partial y)(ln(sqrt(3x)+5y))

\frac{\partial}{\partial y} (ln (3 x + 5 y))

\frac{5}{3 x + 5 y}

Solution steps

\frac{\partial}{\partial y} (ln (3 x + 5 y))

Simplify

ln (3 x + 5 y) : ln (3 x + 5 y)

= \frac{\partial}{\partial y} (ln (3 x + 5 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{3 x + 5 y} \frac{\partial}{\partial y} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{\partial}{\partial y} (3 x + 5 y)

\frac{\partial}{\partial y} (3 x + 5 y) = 5

= \frac{1}{3 x + 5 y} \cdot 5

Simplify

\frac{1}{3 x + 5 y} \cdot 5 : \frac{5}{3 x + 5 y}

= \frac{5}{3 x + 5 y}

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

n = 0 \sum \infty \frac{2}{4 n ^{2} - 1}

\int \frac{x + 2}{x ^{2} + 1} d x

y = 1 - x^{2} arcsin (x)

y^{^{'}} = (x^{2})

What is (\partial)/(\partial y)(ln(sqrt(3x)+5y)) ?
The answer to (\partial)/(\partial y)(ln(sqrt(3x)+5y)) is 5/(sqrt(3)\sqrt{x)+5y}