How do you calculator the derivative for #(2x-5)/(x^(2)-4)#?

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How do you calculator the derivative for #(2x-5)/(x^(2)-4)#?

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Answer 1 · 2015-05-23T16:42:47

The quotient rule says that for some #h(x) = f(x)/(g(x))#, the derivative is:

#h'(x) = [g(x)f'(x) - f(x)g'(x)]/(g(x))^2#

so we get:

#h'(x) = [(x^2-4)(2) - (2x-5)(2x)]/(x^2-4)^2 = (2x^2- 8 - 4x^2 + 10x)/(x^2-4)^2#
#= (-2x^2+10x-8)/(x^2-4)^2#
#= [(-2x + 2)(x - 4)]/(x^2-4)^2 = [2(-x+1)(x - 4)]/(x^2-4)^2#

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How do you calculator the derivative for #(2x-5)/(x^(2)-4)#?

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