What is (\partial)/(\partial y)(sqrt(3x+4y)) ?

The answer to (\partial)/(\partial y)(sqrt(3x+4y)) is 2/(sqrt(3x+4y))

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(\partial)/(\partial y)(sqrt(3x+4y))

\frac{\partial}{\partial y} (3 x + 4 y)

\frac{2}{3 x + 4 y}

Solution steps

\frac{\partial}{\partial y} (3 x + 4 y)

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 3 x + 4 y} \frac{\partial}{\partial y} (3 x + 4 y)

= \frac{1}{2 3 x + 4 y} \frac{\partial}{\partial y} (3 x + 4 y)

\frac{\partial}{\partial y} (3 x + 4 y) = 4

= \frac{1}{2 3 x + 4 y} \cdot 4

Simplify

\frac{1}{2 3 x + 4 y} \cdot 4 : \frac{2}{3 x + 4 y}

= \frac{2}{3 x + 4 y}

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

\frac{d}{d x} ([x + (x + sin^{2} (x))^{3}]^{6})

\int 2^{e^{x}} (1 + 2^{e^{x}})^{5} e^{x} d x

\frac{d}{d x} (\frac{sec ( x )}{x})

\frac{d}{d x} ((ln (3))^{x})

What is (\partial)/(\partial y)(sqrt(3x+4y)) ?
The answer to (\partial)/(\partial y)(sqrt(3x+4y)) is 2/(sqrt(3x+4y))