What is (\partial)/(\partial y)(x/(sqrt(yz))) ?

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

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(\partial)/(\partial y)(x/(sqrt(yz)))

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

- \frac{x}{2 y ^{\frac{3}{2}} z ^{\frac{1}{2}}}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

= x \frac{\partial}{\partial y} (\frac{1}{yz})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (yz) = z

= x (- \frac{1}{2 ( yz ) ^{\frac{3}{2}}} z)

Simplify

x (- \frac{1}{2 ( yz ) ^{\frac{3}{2}}} z) : - \frac{x}{2 y ^{\frac{3}{2}} z ^{\frac{1}{2}}}

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

\int_{1}^{9} x - 1 d x

\frac{d}{d x} (8 x + 3)

x \to 0 + lim (x^{t a n (x^{2})})

\frac{\partial}{\partial x} (2 k x^{2} y^{2} - x sin (y))

\frac{2 e ^{- 2 s}}{s ^{2} - 4}

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