What is (\partial)/(\partial x)((2pir^{3/2})/(sqrt(yx))) ?

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

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(\partial)/(\partial x)((2pir^{3/2})/(sqrt(yx)))

\frac{\partial}{\partial x} (\frac{2 π r ^{\frac{3}{2}}}{y x})

- \frac{π r ^{\frac{3}{2}}}{y ^{\frac{1}{2}} x ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 π r ^{\frac{3}{2}}}{y x})

Treat

r, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 π r^{\frac{3}{2}} \frac{\partial}{\partial x} (\frac{1}{y x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 2 π r^{\frac{3}{2}} \frac{\partial}{\partial x} ((y x)^{- \frac{1}{2}})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y x) = y

= 2 π r^{\frac{3}{2}} (- \frac{1}{2 ( y x ) ^{\frac{3}{2}}} y)

Simplify

2 π r^{\frac{3}{2}} (- \frac{1}{2 ( y x ) ^{\frac{3}{2}}} y) : - \frac{π r ^{\frac{3}{2}}}{y ^{\frac{1}{2}} x ^{\frac{3}{2}}}

= - \frac{π r ^{\frac{3}{2}}}{y ^{\frac{1}{2}} x ^{\frac{3}{2}}}

y = x, y = 2 x 81 - x^{2}

\int \frac{1}{( x ^{2} - 1 ) ^{2}} d x

\frac{\partial}{\partial y} (7 x^{4 y})

(x - 5) e^{(x)} + 5

f (x) = 6 - x, at x = - 3

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