baldymcgee6
Easiest way to go about taking this derivative?
Power rule, chain rule and quotient rule is kind of ugly.



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baldymcgee6
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\[f(x) =\sqrt{\frac{ x1}{ x+1}}\]

irkiz
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chain rule first then quotient rule

irkiz
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and it isnt ugly at all. The higher u go, the more 'uglier' it gets. dont be afraid of 'ugly' solutions

baldymcgee6
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oops supposed to be 1x and 1+x

irkiz
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still doesnt matter just flip the sings

irkiz
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dw:1353220538034:dw

irkiz
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chain rule the exponent 1/2 then differentiate the one inside the bracket using quotient rule

baldymcgee6
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dw:1353220581666:dw

irkiz
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yup

baldymcgee6
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that's ugly.

irkiz
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it really isnt ugly at all... i have seen even uglier ones at my level

irkiz
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just make the exponent 1/2 into a square root and put it beside the (1+x) ^2

irkiz
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same with the 2 in the denominator

baldymcgee6
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This is for a first derivative analysis... It is ugly to find zeroes.

irkiz
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dw:1353220820451:dw

baldymcgee6
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dw:1353220855332:dw

irkiz
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what are you trying to find?

baldymcgee6
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first and second derivative analysis

irkiz
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for turning points and maximum/minimum?

baldymcgee6
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max, min, inflections

irkiz
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no solution then

baldymcgee6
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there is a min at x=1