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

The answer to (\partial)/(\partial x)(1/(2x^{1/2)}) is -1/(4x^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \frac{1}{4 x ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= \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}

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

Simplify

\frac{1}{2} (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{1}{4 x ^{\frac{3}{2}}}

= - \frac{1}{4 x ^{\frac{3}{2}}}

y = 20 x

y^{^{'''}} - 2 y^{^{''}} - y + 2 y = 0

x \to 0 lim (\frac{3 x ^{2} - 8 x}{x})

f (x) = \frac{7 + 2 ln ( x )}{x}

f (x) = x^{2} - 6, (- 2, - 2)

What is (\partial)/(\partial x)(1/(2x^{1/2)}) ?
The answer to (\partial)/(\partial x)(1/(2x^{1/2)}) is -1/(4x^{3/2)}