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Calculus Question

Differentiate y = (2x+5)^3(6x-1)^5. Express your answer in factored form.
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1 Answer

Hi Don,
In order to discuss this easily let f(x) = (2x+5)3 and g(x) = (6x-1)5.
So we are going to use the product rule fg' + gf'.
fg' = (2x+5)3 5(6x-1)4 (6)  (note the use of the chain rule to get that factor of 6) -- also, (5)(6) = 30
gf' = (6x-1)5 3(2x+5)2 (2)  (chain rule again to get that factor of 2) -- also, (2)(3) = 6
Write those expressions separated by a plus (+ ) sign. You will be able to factor out the GCF from each term and simplify.
I can see factoring out something like 6(2x+5)2(6x-1)4 [ leaving it up to you as to what goes in here]