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

The answer to (\partial)/(\partial x)(sqrt(4x+4y)) is 1/(sqrt(x+y))

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

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

\frac{1}{x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x + y}

\frac{\partial ^{2}}{\partial u ( w ) \partial w} (e^{u (w) - w})

\int \frac{1}{( x - 1 ) ( x ^{2} + 9 )} d x

\int \frac{1}{9 - 4 x} d x

y = \frac{- 12}{4 x}

2 x + y + (x + 2 y) y^{^{'}} = 0

What is (\partial)/(\partial x)(sqrt(4x+4y)) ?
The answer to (\partial)/(\partial x)(sqrt(4x+4y)) is 1/(sqrt(x+y))