Differentiate the function. f(x)=((3x-4)/(2x+2))^-5?

?2015-02-19T04:54:35Z

f(x) = ((3x - 4)/(2x + 2))⁻⁵ => ((2x + 2)/(3x - 4))⁵

=> (2x + 2)⁵/(3x - 4)⁵

Now, if f(x) = u/v, f '(x) = (u'v - uv')/v²

so, u = (2x + 2)⁵, so u' = 10(2x + 2)⁴

and v = (3x - 5)⁵, so v' = 15(3x - 5)⁴

Hence, f '(x) => [10(2x + 2)⁴(3x - 5)⁵ - 15(3x - 5)⁴(2x + 2)⁵]/(3x - 5)¹⁰

or, 5(2x + 2)⁴(3x - 5)⁴[2(3x - 5) - 3(2x + 2)]/(3x - 5)¹⁰

=> 5(2x + 2)⁴(3x - 5)⁴[-16]/(3x - 5)¹⁰

i.e. f '(x) = -80(2x + 2)⁴/(3x - 5)⁶

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