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

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

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(\partial)/(\partial y)(ln(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))

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}

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

\frac{\partial}{\partial y} (x^{7} + 2^{y} + x^{y})

f (x) = 2 θ - 2 sin (θ)

f (x) = \frac{6}{x}, at x = - 2

(7 x + 1)^{2}

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