What is the d/(dt)(1/(12sqrt(t))) ?

The d/(dt)(1/(12sqrt(t))) is -1/(24t^{3/2)}

What is the first d/(dt)(1/(12sqrt(t))) ?

The first d/(dt)(1/(12sqrt(t))) is -1/(24t^{3/2)}

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\frac{d}{d t} (\frac{1}{12 t})

- \frac{1}{24 t ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{1}{12 t})

Take the constant out:

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

= \frac{1}{12} \frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

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

= \frac{1}{12} \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}{12} (- \frac{1}{2} t^{- \frac{1}{2} - 1})

Simplify

\frac{1}{12} (- \frac{1}{2} t^{- \frac{1}{2} - 1}) : - \frac{1}{24 t ^{\frac{3}{2}}}

= - \frac{1}{24 t ^{\frac{3}{2}}}

What is the d/(dt)(1/(12sqrt(t))) ?
The d/(dt)(1/(12sqrt(t))) is -1/(24t^{3/2)}
What is the first d/(dt)(1/(12sqrt(t))) ?
The first d/(dt)(1/(12sqrt(t))) is -1/(24t^{3/2)}