What is the derivative of 2/(sqrt(65+4t)) ?

The derivative of 2/(sqrt(65+4t)) is -4/((65+4t)^{3/2)}

What is the first derivative of 2/(sqrt(65+4t)) ?

The first derivative of 2/(sqrt(65+4t)) is -4/((65+4t)^{3/2)}

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derivative of

\frac{2}{65 + 4 t}

- \frac{4}{( 65 + 4 t ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{2}{65 + 4 t})

Take the constant out:

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

= 2 \frac{d}{d t} (\frac{1}{65 + 4 t})

Apply exponent rule:

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

= 2 \frac{d}{d t} ((65 + 4 t)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 65 + 4 t ) ^{\frac{3}{2}}} \frac{d}{d t} (65 + 4 t)

= - \frac{1}{2 ( 65 + 4 t ) ^{\frac{3}{2}}} \frac{d}{d t} (65 + 4 t)

\frac{d}{d t} (65 + 4 t) = 4

= 2 (- \frac{1}{2 ( 65 + 4 t ) ^{\frac{3}{2}}} \cdot 4)

Simplify

2 (- \frac{1}{2 ( 65 + 4 t ) ^{\frac{3}{2}}} \cdot 4) : - \frac{4}{( 65 + 4 t ) ^{\frac{3}{2}}}

= - \frac{4}{( 65 + 4 t ) ^{\frac{3}{2}}}

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What is the derivative of 2/(sqrt(65+4t)) ?
The derivative of 2/(sqrt(65+4t)) is -4/((65+4t)^{3/2)}
What is the first derivative of 2/(sqrt(65+4t)) ?
The first derivative of 2/(sqrt(65+4t)) is -4/((65+4t)^{3/2)}