Question

Can someone explain how to find the derivative of :

1. y= 5^ãx / x

And the second derivative of:
y= xe^10x

For this question I got up to the first derivative and got this
y = e^10x + 10xe^10x but I can't seem to get the correct answer for the second derivative.

Answer 1

, its suppose to be

5^squarerootx / x

Answer 2

y = (5^(√x))/x

I would take ln of both sides
lny = ln (5^(√x))/x
lny = √x(ln5) - lnx
lny = (ln5)(x^1/2) - lnx

y' / y = (1/2)ln5(x^(-1/2)) - 1/x

y = [(5^(√x))/x][(1/2)ln5(x^(-1/2)) - 1/x]
(what a mess!)

for y = xe^10x
y' = e^10x + 10xe^10x is correct, now do it again
y'' = 10e^10x + 10(e^10x + 10xe^10x) , we just did that last part
= 20e^10x = 100xe^10x