Solve this derivative using the quotient rule

Mathematics

1 answer:

LekaFEV [45]3 years ago

7 0

$\bf y=\cfrac{(-x+5)^5}{3x-4}\implies y=\cfrac{(5-x)^5}{3x-4}
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\cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{5(5-x)^4(-1)(3x-4)~~-~~(5-x)^5(3)}{(3x-4)^2}}
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\cfrac{dy}{dx}=\cfrac{-5(5-x)^4(3x-4)-3(5-x)^5}{(3x-4)^2}
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\cfrac{dy}{dx}=\cfrac{\stackrel{common~factor}{-(5-x)^4}[5(3x-4)+3(5-x)]}{(3x-4)^2}
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\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[15x-20+15-3x]}{(3x-4)^2}
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\cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[12x-5]}{(3x-4)^2}\implies \cfrac{dy}{dx}=\cfrac{(5-x)^4~~[5+12x]}{(3x-4)^2}$

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