Answer:
9x²ln(x)
Step-by-step explanation:
Integral of ln(t) with respect to t is:
t×ln(t) - t
Upper limit- lower limit:
x³×ln(x³) - x³ - 0
Note: ln(x³) = 3ln(x)
F(x) = x³ × 3ln(x) - x³
F(x) = 3x³ln(x) - x³ = x³(3ln(x) - 1)
F'(x) = 3x²(3ln(x) - 1) + x³(3/x)
= 3x²(3ln(x) - 1) + 3x²
= 3x²(3ln(x) - 1 + 1)
F'(x) = 9x²ln(x)
