Calculus Question

Question

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

Answer 1

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]