How do you find the derivative of #f(x)=(6-5x)^-1#?

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Answer 1 · 2016-04-08T16:38:34

#f'(x) = 5/(6-5x)^2#

Use the chain rule, where if

#f(x) = g(h(x))#

then

#f'(x) = h'(x)g'(h)#.

If we say then that #h(x) = 6 - 5x# and #g(x) = h^-1#,

#h'(x) = -5#
#g'(h) = -1/h^2 = -1/(6-5x)^2#

then

#f'(x) = 5/(6-5x)^2#