URGENT Linearisation and Fundamental Theorem of Calculus question, PLEASE HELP...

Question

anonymous · Answer

I don't how I can find the derivative of the equation above for the linearisation. Am I supposed to use chain rule for the differentation of the weird integral looking part of the function?

mendicant_bias · Answer

(?)

mendicant_bias · Answer

Are you trying to take the derivative of g(x) with respect to x?

mendicant_bias · Answer

And you're confused about the lower and upper bounds being in terms of x while the integrand is with respect to t, and how to get it in the right form, I'm guessing?

anonymous · Answer

Yes, I'm confused about how to take the derivative of g(x) with respect to x. There is an x variable there. Am I supposed to use the product rule for differentiation?

mendicant_bias · Answer

I haven't done FTC problems in forever and honestly won't be much immediate help; I would like to say that yes, the product rule should be used, but I can see why you would be confused after that. I'm reviewing stuff to see if I figure out how to do this again.

mendicant_bias · Answer

I've literally never seen an FTC problem like that. Still looking for a similar example. Good question, OP.

anonymous · Answer

Let $F(x) = \int_0^x sec(t-1)\ dt$ and then
$g(x) = 3+ x(F(x^2) - F(1) = 3 + xF(x^2) - xF(1)$
Now apply the product rule, chain rule and fundamental theorem of calculus.