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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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