How do you find the derivatives of #f(x) = (2x-3) ^ -2#?

1 Answer
Alan P.
Apr 27, 2015

One way to approach this problem is to let
#f(x) = g(h(x))#
where
#g(x) = x^(-2)#
and
#h(x) = 2x-3#

By the Chain Rule
#(df(x))/(dx) = color(red)((d g(h(x)))/(d h(x))) * color(blue)((d h(x))/(dx))#

#= color(red)(-2(h(x))^(-3)) * color(blue)(2)#

#= color(red)(-2(2x-3)^(-3)) * color(blue)(2)#

#= - 4/((2x-3)^3)#

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