We have to find the second derivative of y = e^5x + (ln x) / 2x

y = e^5x + (ln x) / 2x

=> y = e^5x + (1/2)(ln x)*(1/x)

y' = 5*e^5x + (1/2)[(-1)(x^-2)(ln x) + (1/x^2)]

y'' = 25*e^5x + (1/2)[2*(x^-3)*ln x - x^-3 - 2/x^3]

y''...

## See

This Answer NowStart your **subscription** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have to find the second derivative of y = e^5x + (ln x) / 2x

y = e^5x + (ln x) / 2x

=> y = e^5x + (1/2)(ln x)*(1/x)

y' = 5*e^5x + (1/2)[(-1)(x^-2)(ln x) + (1/x^2)]

y'' = 25*e^5x + (1/2)[2*(x^-3)*ln x - x^-3 - 2/x^3]

y'' = 25*e^5x + (1/2)[2*ln x / x^3 - 3/ x^3]

y'' = 25*e^5x + (ln x) / (x^3) - (3/2)*(1/x^3)

**The required second derivative is: 25*e^5x + (ln x)/(x^3) - (3/2)*(1/x^3)**