What is (\partial)/(\partial x)(1/(2x^{5/2 y^{1/2)}}) ?

The answer to (\partial)/(\partial x)(1/(2x^{5/2 y^{1/2)}}) is -(5x^{(-5y^{1/2}-2)/2}y^{1/2})/(4)

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(\partial)/(\partial x)(1/(2x^{5/2 y^{1/2)}})

\frac{\partial}{\partial x} (\frac{1}{2 x ^{\frac{5}{2} y^{\frac{1}{2}}}})

- \frac{5 x ^{\frac{- 5 y ^{\frac{1}{2}} - 2}{2}} y ^{\frac{1}{2}}}{4}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2 x ^{\frac{5}{2} y^{\frac{1}{2}}}})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial x} (\frac{1}{x ^{\frac{5}{2} y^{\frac{1}{2}}}})

Apply exponent rule:

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

= \frac{1}{2} \frac{\partial}{\partial x} (x^{- \frac{5}{2} y^{\frac{1}{2}}})

Apply the Power Rule:

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

= \frac{1}{2} (- \frac{5}{2} y^{\frac{1}{2}} x^{- \frac{5}{2} y^{\frac{1}{2}} - 1})

Simplify

\frac{1}{2} (- \frac{5}{2} y^{\frac{1}{2}} x^{- \frac{5}{2} y^{\frac{1}{2}} - 1}) : - \frac{5 x ^{\frac{- 5 y ^{\frac{1}{2}} - 2}{2}} y ^{\frac{1}{2}}}{4}

= - \frac{5 x ^{\frac{- 5 y ^{\frac{1}{2}} - 2}{2}} y ^{\frac{1}{2}}}{4}

e^{2 t} sin (5 t) cos (3 t)

x \to 0 + lim (\frac{5}{x ^{2} - x})

x^{2}, x^{3}, 0, 1

\int t (3 t + 2)^{\frac{3}{2}} d t

\int cos^{2} (t) d t

What is (\partial)/(\partial x)(1/(2x^{5/2 y^{1/2)}}) ?
The answer to (\partial)/(\partial x)(1/(2x^{5/2 y^{1/2)}}) is -(5x^{(-5y^{1/2}-2)/2}y^{1/2})/(4)