Question

d/dx {((X^2)+1)((X^2)+2)/((x^3)+1)((x^3)+2)} Is there an easier way to do this other than multiplying it all out and then using quotient rule?

Answer 1

take logarithm

Answer 2

Thats what I was thinking but I wasnt at class for that. How would taking the logarithm go exactly?

Answer 3

\[\ln y=\ln \left( x^2+1 \right)+\ln \left( x^2+2 \right)-\ln \left( x^3+1 \right)-\ln \left( x^3+2 \right)\]

Answer 4

\[\frac{ 1 }{ y }\frac{ dy }{ dx }=\frac{ 2x }{ x^2+1 }+?\]

Answer 5

and then the derivative of each would simply be 1/whatever is in the parantheses

Answer 6

Thank you

Answer 7

then take y to R.H.S and put the value of y

Answer 8

Thank you