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

The answer to (\partial)/(\partial y)(sqrt(5x+4y)) is 2/(sqrt(5x+4y))

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

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

\frac{2}{5 x + 4 y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

= \frac{1}{2 5 x + 4 y} \frac{\partial}{\partial y} (5 x + 4 y)

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

= \frac{1}{2 5 x + 4 y} \cdot 4

Simplify

\frac{1}{2 5 x + 4 y} \cdot 4 : \frac{2}{5 x + 4 y}

= \frac{2}{5 x + 4 y}

\frac{d}{d x} (\frac{7}{x + 1})

\int_{1}^{5} w^{2} ln (w) d w

\int \frac{{ y }}{L { y }} d L

\frac{5}{( x ^{2} + 1 )}

\int 1 + cos (2 θ) d θ

What is (\partial)/(\partial y)(sqrt(5x+4y)) ?
The answer to (\partial)/(\partial y)(sqrt(5x+4y)) is 2/(sqrt(5x+4y))