calculating derivative by definition

[Dorian Gray]

Greetings Mathematicians,


I was wondering if someone could please aid me with this problem.

Find the derivative of g(x)= 1/ [squareroot of (1 +2x)] using the standard definition of a derivative ( I am using the [f(a+h) - f(a)]/[h] ).

I am not sure how to start the problem. I attached a copy of my work so far.

 

[daon2]

This is similar to the last one you posted.

Multiply the top and bottom by \(\displaystyle \sqrt{1+2(a+h)} +\sqrt{1+2a}\)

You should be able to do this one now.

 

[Dorian Gray]

thank you

Thank you Mathematician Daon2. Would you say that anytime you have a situation with 2 square root terms with a plus or minus between them that the best method would be to use the conjugate?


Thanks again.

 

[daon2]

Thank you Mathematician Daon2. Would you say that anytime you have a situation with 2 square root terms with a plus or minus between them that the best method would be to use the conjugate?


Thanks again.

It depends entirely on the situation. Though in a calculus course it is one of those "tricks" commonly used with radicals.