How to find f '(a). f(x) = √ 2-6x ?

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How to find f '(a). f(x) = √ 2-6x ?

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Answer 1 · 2015-03-03T19:57:42

If $f (x) = \sqrt{2 - 6 x}$ $f(x) = sqrt( 2 - 6x)$

Define $h (x) = 2 - 6 x$ $h(x) = 2 - 6x$
and $g (x) = \sqrt{x} = x^{\frac{1}{2}}$ $g(x) = sqrt(x) = x^(1/2)$
so
$f (x) = g (h (x)$ $f(x) = g(h(x)$

Use the product rule:
$\frac{d f (x)}{d x} = \frac{d g (h (x))}{d h (x)} \cdot \frac{d h (x)}{d x}$ $(d f(x))/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)$

$= ((\frac{1}{2}) \cdot {(2 - 6 x)}^{- \frac{1}{2}}) \cdot (- 6)$ $= ((1/2) * (2 - 6x)^(-1/2)) * (-6)$

$= \frac{- 3}{\sqrt{2 - 6 x}}$ $= (-3)/(sqrt(2-6x))$

So,
$f'(a) = (-3)/(sqrt(2-6a))$

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How to find f '(a). f(x) = √ 2-6x ?

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