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

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

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(\partial)/(\partial x)(yln(3x+5y))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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