What is the derivative of 1/(sqrt(x+8)) ?

The derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

What is the first derivative of 1/(sqrt(x+8)) ?

The first derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

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derivative of

\frac{1}{x + 8}

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x + 8})

Apply exponent rule:

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

= \frac{d}{d x} ((x + 8)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1

Simplify

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}}

\int (tan^{2} (x) + 1) d x

f (x) = 9 sin (3 x)

\frac{d}{d y} (x + y^{2})

\int x 2 - x^{2} - x^{2} d x

\frac{d y}{d x} = \frac{sec ( y )}{( x - 4 ) ^{2}}

What is the derivative of 1/(sqrt(x+8)) ?
The derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}
What is the first derivative of 1/(sqrt(x+8)) ?
The first derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}