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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{s}{s + a}

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\int \frac{sin ^{7} ( 5 x )}{cos ^{4} ( 5 x )} d x

\frac{d}{d t} (e^{t} cos (t))

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