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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(16, - 2), (15, 86)

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