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

d er i v a t i v e \frac{( ( x + 1 ) ( x + 2 ) )}{x}

x \to - 3 + lim (\frac{- 5 x}{x + 3})

\int_{0}^{1} x 3^{x} d x

2 x d y + y d x = 0

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)}