What is (\partial)/(\partial y)(sqrt(3x+2y)) ?

The answer to (\partial)/(\partial y)(sqrt(3x+2y)) is 1/(sqrt(3x+2y))

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(\partial)/(\partial y)(sqrt(3x+2y))

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

\frac{1}{3 x + 2 y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{8 + x f ( x )}{x})

\int sin (x) \frac{1}{x} d x

\frac{\partial}{\partial y} (2 x^{2} + 2 y^{2})

\frac{d y}{d x} = x \cdot e^{- 2 x}, y (0) = 3

What is (\partial)/(\partial y)(sqrt(3x+2y)) ?
The answer to (\partial)/(\partial y)(sqrt(3x+2y)) is 1/(sqrt(3x+2y))