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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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