What is (\partial)/(\partial x)(80x^{1/2}z^{1/2}) ?

The answer to (\partial)/(\partial x)(80x^{1/2}z^{1/2}) is (40z^{1/2})/(x^{1/2)}

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(\partial)/(\partial x)(80x^{1/2}z^{1/2})

\frac{\partial}{\partial x} (80 x^{\frac{1}{2}} z^{\frac{1}{2}})

\frac{40 z ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (80 x^{\frac{1}{2}} z^{\frac{1}{2}})

Treat

z

as a constant

Take the constant out:

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

= 80 z^{\frac{1}{2}} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 80 z^{\frac{1}{2}} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

80 z^{\frac{1}{2}} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{40 z ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

= \frac{40 z ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

y = x^{2}, y = 2 x + 3

\int_{0}^{8} \frac{7}{3} x d x

x \to 0 lim (\frac{2}{3 cos ( x )})

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

x \to 0 lim (\frac{x}{2 x + sin ( x )})

What is (\partial)/(\partial x)(80x^{1/2}z^{1/2}) ?
The answer to (\partial)/(\partial x)(80x^{1/2}z^{1/2}) is (40z^{1/2})/(x^{1/2)}