calculus question

Question

Let  . Use your calculator to find F"(1).

	12
	6
	4

Answer 1

Use log rules to change ln(t²) to 2lnt.

By the 2nd FTC, F ' (x) = 6ln(3x).

Then, F " (x) = 6/x and F " (1) = 6.

Using a TI calculator, you would enter it as d/dx[d/dx(∫₁^3xln(x²)dx)|_x=x)|_x=1