Question

Find the first and second derivatives of the function.
y = e^6x * sin(5x) (i found the first derivative, i just need help with second derivative)

Answer 1

y' = 6 *e^6x * sin(5x) + e^6x * cos(5x) * 5
y' =(6* sin(5x) + 5* cos(5x) ) e^6x

y''= 6 {6*e^6x * sin(5x) +5*e^6x*cos(5x) } + 5{6*e^6x * cos(5x) - 5*e^6x * sin(5x) }
y" = 36*e^6x * sin(5x) + 30*e^6x*cos(5x) +30*e^6x * cos(5x) - 25*e^6x * sin(5x)
y''= 11*e^6x * sin(5x) + 60*e^6x*cos(5x)

Answer 2

THANK U!!!!!

Answer 3

i appreciate u showing each step

Answer 4

your very welcome!

Answer 5

\[yy'+y=o\]