From first principles (limiting process), find the derivative of ;
y= 2/( x^4 +1) + 3/ x
I would greatly appreciate this help... I tried to work it out but it's confusing and long. Please show details.
Hello, thaliaj_df!
This is a messy problem . . .
They could have easily made two problems out of it.
I must assume that you know the four steps of the First Principles:From first principles, find the derivative of: .
. . (1) Find . . . Replace with ... and simplify.
. . (2) Subtract . . . Subtract the original function ... and simplify.
. . (3) Divide by . . . Factor and reduce.
. . (4) Take the limit as . . . Let and see "what's left."
We will differentiate the two fractions separately . . .
Let
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . . . . .
Hence: .
Let
Hence: .
Therefore: .