What is (\partial)/(\partial y)(sqrt((x+5)/(y+1))) ?

The answer to (\partial)/(\partial y)(sqrt((x+5)/(y+1))) is -(sqrt(x+5))/(2(y+1)^{3/2)}

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(\partial)/(\partial y)(sqrt((x+5)/(y+1)))

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

- \frac{x + 5}{2 ( y + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{x + 5}{y + 1}} (- \frac{x + 5}{( y + 1 ) ^{2}}) : - \frac{x + 5}{2 ( y + 1 ) ^{\frac{3}{2}}}

= - \frac{x + 5}{2 ( y + 1 ) ^{\frac{3}{2}}}

\int e^{x} x^{- 2} d x

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

\int x 1 - 3 x d x

f (x) = \frac{1}{( x - 5 ) ^{2}}, at x = - 3

\int - sin (5 x) d x

What is (\partial)/(\partial y)(sqrt((x+5)/(y+1))) ?
The answer to (\partial)/(\partial y)(sqrt((x+5)/(y+1))) is -(sqrt(x+5))/(2(y+1)^{3/2)}