What is the derivative of f(t)= 1/(sqrt(t)) ?

The derivative of f(t)= 1/(sqrt(t)) is -1/(2t^{3/2)}

What is the first derivative of f(t)= 1/(sqrt(t)) ?

The first derivative of f(t)= 1/(sqrt(t)) is -1/(2t^{3/2)}

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derivative of

f (t) = \frac{1}{t}

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

Solution steps

\frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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What is the derivative of f(t)= 1/(sqrt(t)) ?
The derivative of f(t)= 1/(sqrt(t)) is -1/(2t^{3/2)}
What is the first derivative of f(t)= 1/(sqrt(t)) ?
The first derivative of f(t)= 1/(sqrt(t)) is -1/(2t^{3/2)}