What is (\partial)/(\partial x)(sqrt((x+5)/(y+2))) ?

The answer to (\partial)/(\partial x)(sqrt((x+5)/(y+2))) is 1/(2sqrt(x+5)\sqrt{y+2)}

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(\partial)/(\partial x)(sqrt((x+5)/(y+2)))

\frac{\partial}{\partial x} (\frac{x + 5}{y + 2})

\frac{1}{2 x + 5 y + 2}

Solution steps

\frac{\partial}{\partial x} (\frac{x + 5}{y + 2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x + 5}{y + 2}} \frac{\partial}{\partial x} (\frac{x + 5}{y + 2})

= \frac{1}{2 \frac{x + 5}{y + 2}} \frac{\partial}{\partial x} (\frac{x + 5}{y + 2})

\frac{\partial}{\partial x} (\frac{x + 5}{y + 2}) = \frac{1}{y + 2}

= \frac{1}{2 \frac{x + 5}{y + 2}} \cdot \frac{1}{y + 2}

Simplify

\frac{1}{2 \frac{x + 5}{y + 2}} \cdot \frac{1}{y + 2} : \frac{1}{2 x + 5 y + 2}

= \frac{1}{2 x + 5 y + 2}

\int \frac{1}{8 x ^{3}} d x

\int \frac{x ^{5} - x + 2}{x ^{2} - x} d x

y = \frac{1}{5} x^{2} - \frac{6}{5} x + \frac{7}{5}, (- 5, 5)

x \to - 1 lim (e^{x - 2})

What is (\partial)/(\partial x)(sqrt((x+5)/(y+2))) ?
The answer to (\partial)/(\partial x)(sqrt((x+5)/(y+2))) is 1/(2sqrt(x+5)\sqrt{y+2)}