What is the derivative of 9/(sqrt(x-6)) ?

The derivative of 9/(sqrt(x-6)) is -9/(2(x-6)^{3/2)}

What is the first derivative of 9/(sqrt(x-6)) ?

The first derivative of 9/(sqrt(x-6)) is -9/(2(x-6)^{3/2)}

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derivative of

\frac{9}{x - 6}

- \frac{9}{2 ( x - 6 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{9}{x - 6})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x - 6})

Apply exponent rule:

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

= 9 \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

= 9 (- \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

9 (- \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{9}{2 ( x - 6 ) ^{\frac{3}{2}}}

= - \frac{9}{2 ( x - 6 ) ^{\frac{3}{2}}}

\int_{1}^{5} 1 + (4)^{2} d x

\frac{d}{d x} (\frac{3}{2 x})

x \to 1 lim (- 3 a x + b)

\frac{d}{d x} ((13 x^{2} - 26 x + 26) e^{x})

\frac{d}{d x} (e^{\frac{x}{2}} + 4 x)

What is the derivative of 9/(sqrt(x-6)) ?
The derivative of 9/(sqrt(x-6)) is -9/(2(x-6)^{3/2)}
What is the first derivative of 9/(sqrt(x-6)) ?
The first derivative of 9/(sqrt(x-6)) is -9/(2(x-6)^{3/2)}