What is (\partial)/(\partial x)(z/(ysqrt(x))) ?

The answer to (\partial)/(\partial x)(z/(ysqrt(x))) is -z/(2yx^{3/2)}

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(\partial)/(\partial x)(z/(ysqrt(x)))

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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

f (z) = \frac{z - 4}{z + 4}

\frac{\partial}{\partial x} (x ln (z^{2} + x^{7}))

\frac{d}{d x} (x^{4} e^{- x})

\frac{d}{d x} ((csc (x) + cot (x))^{- 1})

What is (\partial)/(\partial x)(z/(ysqrt(x))) ?
The answer to (\partial)/(\partial x)(z/(ysqrt(x))) is -z/(2yx^{3/2)}