How to find the third deriavative of this function using leibniz theorem?

Question

Using leibniz theorem find the third derivative of this following function

y= e^2xlnx

Answer 1

Let A = e^2x; B = lnx; A₁ = 2e^2x; B₁ = 1/x; A₂ = 4e^2x; B₂ = - 1/x²; A₃= 8e^2x; B₃ = 2/x³.

(e^2xlnx)^'''' = 8e^2xlnx + 3(4e^2x)(1/x) + 3(2e^2x)(- 1/x²) +e^2x(2/x³) = 8e^2xlnx + 12e^2x/x - 6e^2x/x² + 2e^2x/x³