differentiate

Question

differentiate 

y= (t^3+3t)/(t^2-4t+3)

 

 

i used the quotient rule and got a different answer than the one in the back of my math book and I'm wondering what i did wrong and the steps i need to take to get the correct answer. 

 

i got (t^4-16t^3+18t^2-24t+9)/(t^2-4t+3)^2

 

Answer 1

If y = u/v then in your problem u' = 3t²+3 and v' = 2t-4

 

Then the NUMERATOR of y' is u'v - uv' which is (3t²+3)(t²-4t+3) - (t³+3t)(2t-4).

 

this is a typing nightmare, but I think that you should multiply out these two products to get A - B and then distribute the - into B and then collect 'lile' terms carefully.  Mark M is right...it's going to be wrong without proper sign management!

 

Answer 2

y' = [(t²-4t+3)(3t²+3) - (t³+3t)(2t-4)]/(t²-4t+3)²

 

    = [3t⁴-12t³+9t²+3t²-12t+9-2t⁴-6t²+4t³+12t]/(t²-4t+3)²

 

    = [t⁴-8t³+6t²+9]/(t²-4t+3)²