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)}

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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}}}

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

f^{^{''}} (x) = x^{- 3} + π x^{2} - 2

f (x) = 2 x^{2} - 3 x, at x = 4

\frac{d}{d x} (\frac{4 x}{2 - x ^{2}})

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

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)}