What is (\partial)/(\partial y)(ln(5x+4y)) ?

The answer to (\partial)/(\partial y)(ln(5x+4y)) is 4/(5x+4y)

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(\partial)/(\partial y)(ln(5x+4y))

\frac{\partial}{\partial y} (ln (5 x + 4 y))

\frac{4}{5 x + 4 y}

Solution steps

\frac{\partial}{\partial y} (ln (5 x + 4 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

= \frac{1}{5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

\frac{\partial}{\partial y} (5 x + 4 y) = 4

= \frac{1}{5 x + 4 y} \cdot 4

Simplify

\frac{1}{5 x + 4 y} \cdot 4 : \frac{4}{5 x + 4 y}

= \frac{4}{5 x + 4 y}

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

4 e^{x} + x

\int_{0}^{9} \frac{1}{81 + t ^{2}} d t

x^{8}

\frac{d}{d x} (x (x - 2)^{2})

What is (\partial)/(\partial y)(ln(5x+4y)) ?
The answer to (\partial)/(\partial y)(ln(5x+4y)) is 4/(5x+4y)