What is (\partial)/(\partial x)(((x+2)/(y+1))^{1/2}) ?

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

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(\partial)/(\partial x)(((x+2)/(y+1))^{1/2})

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 ( \frac{x + 2}{y + 1} ) ^{\frac{1}{2}}} \cdot \frac{1}{y + 1} : \frac{1}{2 ( x + 2 ) ^{\frac{1}{2}} ( y + 1 ) ^{\frac{1}{2}}}

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

l a pl a ce t r an s f or m e^{a s}

n \to \infty lim (- 3 + 4 n^{5})

d er i v a t i v e y = ln (9 x^{2} + 5 y^{2})

x \to \infty lim (ln (7 x + 1) - ln (4 x + 1))

\int_{0}^{5} 25 - x^{2} d x

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