Stuck on a differentiation problem

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msd1997

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Where am I going wrong? How to proceed forward?
 

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msd1997 said:
Is this correct now? I was supposed to use chain rule?
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That is fine. I would have used the general power rule to find the derivative of (1+x2)1/2 which is much simpler than using the chain rule. I almost always use the general power rule over the chain rule.
 
Steven G said:
That is fine. I would have used the general power rule to find the derivative of (1+x2)1/2 which is much simpler than using the chain rule. I almost always use the general power rule over the chain rule.
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I thought I used the general power rule, and it turned out to be wrong. Can please tell me how to use the general power rule in this?
 
( f(x)n)' = n*( f(x) )n-1* f'(x)

You left out the f'(x) part which is 2x. Try again.
In the future if you use an allowable method and it does not work out do not try another method. Find out what went wrong with your method and if you like also try another method.
 
Steven G said:
That is fine. I would have used the general power rule to find the derivative of (1+x2)1/2 which is much simpler than using the chain rule. I almost always use the general power rule over the chain rule.
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Steven

I do not understand how to solve this problem without using the chain rule explicitly or implicitly.
 
JeffM said:
Steven

I do not understand how to solve this problem without using the chain rule explicitly or implicitly.
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I explicitly agree with you. The modified power rule (as stated by Steven - response #6) used chain-rule. It is just a matter of semantics - call it whatever -as long as it is applied correctly!!
 
JeffM said:
Steven

I do not understand how to solve this problem without using the chain rule explicitly or implicitly.
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Jeff,
I understand what you are saying. I only say that I am using the chain rule when I formally call something u like the OP did the 2nd time.
 
Subhotosh Khan said:
I explicitly agree with you. The modified power rule (as stated by Steven - response #6) used chain-rule. It is just a matter of semantics - call it whatever -as long as it is applied correctly!!
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Subhotosh, I think it is called the general power rule. I never heard of it being called the modified power rule. Who knows, maybe you are also correct.
 
Steven G said:
Jeff,
I understand what you are saying. I only say that I am using the chain rule when I formally call something u like the OP did the 2nd time.
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Got it. I call that technique u-substitution.

I believe that, some time ago, you indicated some distaste for the substitution method whereas I indicated a fondness for it. You and I are not going to argue about what is just a matter of taste. But I do think some students find substitution helpful in organizing their thoughts.
 
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