What is the derivative of y= 9/(sqrt(x+8)) ?

The derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}

What is the first derivative of y= 9/(sqrt(x+8)) ?

The first derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}

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derivative of

y = \frac{9}{x + 8}

- \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{9}{x + 8})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x + 8})

Apply exponent rule:

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

= 9 \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

= 9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

= - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

What is the derivative of y= 9/(sqrt(x+8)) ?
The derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}
What is the first derivative of y= 9/(sqrt(x+8)) ?
The first derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}