What is the derivative of 2/(sqrt(4x+1)) ?

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

What is the first derivative of 2/(sqrt(4x+1)) ?

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

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\frac{d}{d x} (\frac{2}{4 x + 1})

- \frac{4}{( 4 x + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2}{4 x + 1})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x + 1) = 4

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

Simplify

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

= - \frac{4}{( 4 x + 1 ) ^{\frac{3}{2}}}

\frac{d}{d x} (3 2 x - x^{2})

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