What is (\partial)/(\partial x)(sqrt((x+4)/(y+6))) ?

The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+6))) is 1/(2sqrt(x+4)\sqrt{y+6)}

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(\partial)/(\partial x)(sqrt((x+4)/(y+6)))

\frac{\partial}{\partial x} (\frac{x + 4}{y + 6})

\frac{1}{2 x + 4 y + 6}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 4}{y + 6})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 4}{y + 6}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 6})

= \frac{1}{2 \frac{x + 4}{y + 6}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 6})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 6}) = \frac{1}{y + 6}

= \frac{1}{2 \frac{x + 4}{y + 6}} \cdot \frac{1}{y + 6}

Simplify

\frac{1}{2 \frac{x + 4}{y + 6}} \cdot \frac{1}{y + 6} : \frac{1}{2 x + 4 y + 6}

= \frac{1}{2 x + 4 y + 6}

(4 x - 3)^{\frac{1}{2}}

x y^{^{'}} + y = 3 cos (x)

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 x})

n = 2 \sum \infty \frac{3}{n \cdot ( n + 3 )}

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 7

What is (\partial)/(\partial x)(sqrt((x+4)/(y+6))) ?
The answer to (\partial)/(\partial x)(sqrt((x+4)/(y+6))) is 1/(2sqrt(x+4)\sqrt{y+6)}