What is the derivative of 1/(2sqrt(x+6)) ?

The derivative of 1/(2sqrt(x+6)) is -1/(4(x+6)^{3/2)}

What is the first derivative of 1/(2sqrt(x+6)) ?

The first derivative of 1/(2sqrt(x+6)) is -1/(4(x+6)^{3/2)}

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\frac{d}{d x} (\frac{1}{2 x + 6})

- \frac{1}{4 ( x + 6 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 6})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{1}{x + 6})

Apply exponent rule:

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

= \frac{1}{2} \frac{d}{d x} ((x + 6)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 6 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 6)

= - \frac{1}{2 ( x + 6 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 6)

\frac{d}{d x} (x + 6) = 1

= \frac{1}{2} (- \frac{1}{2 ( x + 6 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

\frac{1}{2} (- \frac{1}{2 ( x + 6 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( x + 6 ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( x + 6 ) ^{\frac{3}{2}}}

\int \frac{1}{4 x ^{2}} d x

\int \frac{- 8 x ^{2}}{4 x - x ^{2}} d x

\frac{d}{d x} (3 cos (x) sin (x))

\int \frac{( x - 2 )}{x} d x

f (x) = 4 x^{3} - 4 x, (- 1, 0)

What is the derivative of 1/(2sqrt(x+6)) ?
The derivative of 1/(2sqrt(x+6)) is -1/(4(x+6)^{3/2)}
What is the first derivative of 1/(2sqrt(x+6)) ?
The first derivative of 1/(2sqrt(x+6)) is -1/(4(x+6)^{3/2)}