What is the derivative of 3/(2sqrt(x-8)) ?

The derivative of 3/(2sqrt(x-8)) is -3/(4(x-8)^{3/2)}

What is the first derivative of 3/(2sqrt(x-8)) ?

The first derivative of 3/(2sqrt(x-8)) is -3/(4(x-8)^{3/2)}

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

- \frac{3}{4 ( x - 8 ) ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

\frac{3}{2} (- \frac{1}{2 ( x - 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{3}{4 ( x - 8 ) ^{\frac{3}{2}}}

= - \frac{3}{4 ( x - 8 ) ^{\frac{3}{2}}}

\int 1 - 2 sin (x) d x

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

\frac{\partial}{\partial x} (ln (x y^{2}))

\frac{\partial}{\partial x} (e^{- x} sin (x^{2} + x y))

\frac{\partial}{\partial u} (u^{2} - v^{2})

What is the derivative of 3/(2sqrt(x-8)) ?
The derivative of 3/(2sqrt(x-8)) is -3/(4(x-8)^{3/2)}
What is the first derivative of 3/(2sqrt(x-8)) ?
The first derivative of 3/(2sqrt(x-8)) is -3/(4(x-8)^{3/2)}