What is the derivative of-x^{1/2} ?

The derivative of-x^{1/2} is -1/(2x^{1/2)}

What is the first derivative of-x^{1/2} ?

The first derivative of-x^{1/2} is -1/(2x^{1/2)}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

- \frac{1}{2} x^{\frac{1}{2} - 1} : - \frac{1}{2 x ^{\frac{1}{2}}}

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

\int e^{x + 2 y} d y

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t (\frac{d y}{d t}) + 22 y = \frac{1}{t}

\frac{\partial}{\partial y} (y ln (y))

\int x^{4} + 1 d x

What is the derivative of-x^{1/2} ?
The derivative of-x^{1/2} is -1/(2x^{1/2)}
What is the first derivative of-x^{1/2} ?
The first derivative of-x^{1/2} is -1/(2x^{1/2)}