Derivatives Math
posted by Mae
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.

Mae
, its suppose to be
5^squarerootx / x 
Reiny
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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