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# Help with First Derivatives watch

1. Hello,

Could someone help me with how to get the answers to these questions:

a) f(x) = 12x / (1+x²)

b) f(x) = ln(1+x²)

Thanks for your time and help
2. for a) you'd use the quotient rule, so if your f(x) is of the form u(x)/v(x), the first derivative is of the form f'(x)= ([v(x)*u'(x)]-[u(x)*v'(x)])/v^2(x)

for b), use the standard result that for a function of the form f(x)=ln g(x), then f'(x)=g'(x)/g(x)

hope that helps and is clear, please say if you dont understand what ive written
3. (Original post by anon2332)
Hello,

Could someone help me with how to get the answers to these questions:

a) f(x) = 12x / (1+x²)

b) f(x) = ln(1+x²)

Thanks for your time and help
You could use the PRODUCT RULE or the Quotient Rule

I prefer the Product Rule

4. Thanks. I think I understand it. What did you get as the final answer.
Cheers
5. how about you say what you got as your answer instead. Is this not a question from a book and so have no answer to compare against?
6. On the first, I prefer to use quotient rule: and are two functions of such that

Therefore

In your question, do you see how we could use and ?

On the second, use the fact that, where is a function of , such that

Then where is the first derivative of .

In your question, do you see how we can use ?

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