Posted by Soroban on August 10, 2002 at 00:22:53:
In Reply to: differentiating posted by bird on August 10, 2002 at 00:07:30:
: how do you differentiate this using differentiating rules i.e. not using logs.
: (x^2+1)(2x^3-3x^2+1)
Golly, bird, you know about Logarithmic Differentiation, but you don't recognize
a PRODUCT when you see one?
In the first week of differentiation, you knew you could multiply it out (Algebra 1 stuff)
and then differentiate:
f(x) = 2x^5 - 3x^4 + 2x^3 - 2x^2 + 1
f'(x) = 10x^4 - 12x^3 + 6x^2 - 4x
In the second week, you learned the Product Rule:
f'(x) = (x^2 + 1)(6x^2 - 6x) + 2x(2x^3 - 3x^2 + 1) = 10x^4 - 12x^3 + 6x^2 - 4x