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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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