Posted by **Mae** on Monday, April 19, 2010 at 8:38pm.

Can someone explain how to find the derivative of :

1. y= 5^x / 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.

- sorry, the first question isnt showing up properly -
**Mae**, Monday, April 19, 2010 at 8:41pm
, its suppose to be

5^squarerootx / x

- Derivatives- Math -
**Reiny**, Monday, April 19, 2010 at 9:48pm
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

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