How to find f '(a). f(x) = √ 2-6x ?

1 Answer
Alan P.
Mar 3, 2015

If #f(x) = sqrt( 2 - 6x)#

Define #h(x) = 2 - 6x#
and #g(x) = sqrt(x) = x^(1/2)#
so
#f(x) = g(h(x)#

Use the product rule:
#(d f(x))/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)#

#= ((1/2) * (2 - 6x)^(-1/2)) * (-6)#

#= (-3)/(sqrt(2-6x))#

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

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