What is the derivative of 1/2 (6t+4)^{-1/2} ?

The derivative of 1/2 (6t+4)^{-1/2} is -3/(2(6t+4)^{3/2)}

What is the first derivative of 1/2 (6t+4)^{-1/2} ?

The first derivative of 1/2 (6t+4)^{-1/2} is -3/(2(6t+4)^{3/2)}

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derivative of

\frac{1}{2} (6 t + 4)^{- \frac{1}{2}}

- \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{1}{2} (6 t + 4)^{- \frac{1}{2}})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d t} ((6 t + 4)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 4)

= - \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \frac{d}{d t} (6 t + 4)

\frac{d}{d t} (6 t + 4) = 6

= \frac{1}{2} (- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \cdot 6)

Simplify

\frac{1}{2} (- \frac{1}{2 ( 6 t + 4 ) ^{\frac{3}{2}}} \cdot 6) : - \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

= - \frac{3}{2 ( 6 t + 4 ) ^{\frac{3}{2}}}

What is the derivative of 1/2 (6t+4)^{-1/2} ?
The derivative of 1/2 (6t+4)^{-1/2} is -3/(2(6t+4)^{3/2)}
What is the first derivative of 1/2 (6t+4)^{-1/2} ?
The first derivative of 1/2 (6t+4)^{-1/2} is -3/(2(6t+4)^{3/2)}