What is the derivative of 1/(u^{1/2)} ?

The derivative of 1/(u^{1/2)} is -1/(2u^{3/2)}

What is the first derivative of 1/(u^{1/2)} ?

The first derivative of 1/(u^{1/2)} is -1/(2u^{3/2)}

derivative of

\frac{1}{u ^{\frac{1}{2}}}

- \frac{1}{2 u ^{\frac{3}{2}}}

Solution steps

\frac{d}{d u} (\frac{1}{u ^{\frac{1}{2}}})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- \frac{1}{2} u^{- \frac{1}{2} - 1} : - \frac{1}{2 u ^{\frac{3}{2}}}

= - \frac{1}{2 u ^{\frac{3}{2}}}

t an g e n t f (x) = 2 x^{2} - 3 x, at x = 4

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

\int_{3}^{5} (- x^{2} + 8 x - 12) d x

x \to 2 lim (3 x + 6)

n = 1 \sum \infty \frac{1}{n ^{\frac{3}{2}}}

What is the derivative of 1/(u^{1/2)} ?
The derivative of 1/(u^{1/2)} is -1/(2u^{3/2)}
What is the first derivative of 1/(u^{1/2)} ?
The first derivative of 1/(u^{1/2)} is -1/(2u^{3/2)}