find the 8th derivative ofe^2x*sin2x?

Answer 1

The first derivative is
2 e^2x*sin2x + 2e^2x*cos2x

The second derivative is
2(2 e^2x*sin2x + 2e^2x*cos2x)
+ 2(2e^2x*cos2x -2e^2xsin2x)
= 8 e^2x*cos2x

Look for a pattern. The fourth derivative might be 8^4 times the original function. Then that would repeat after the eighth derivative

Answer 2

help me with this find higher derivative (d^2 y)/(dx^2 ) y=2x^5+3sin2x-4x+cos2x+ln2x^5