Advanced Math/Derivative

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Expert: Robi Bhattacharjee - 9/2/2008


Question
I'm having trouble with one of my math problems and the answer is not in the back. Can you help?

tan^-1(sqrt(7x^2-1))

Answer
Hello Tim,

I must say that this definetly is a challenging question. So in order to do this problem, you have to use the chain rule.

So first we need to differientiate 7x^2 - 1. This  is simply 14x by using the formula.

Now sqrt(7x^2 - 1), to differeientiate this, we find the derivative of sqrt(u) where u = 7x^2 - 1 and multiply it by 14x. So this is

14x * 1 /2sqrt(u) = 7x/sqrt(7x^2 - 1) Now to differientiate tan^-1 of this. We differeientiate tan^-1(u) where u = sqrt(7x^2 - 1) and multiply it by 7x/sqrt(7x^2 -1).

So this equals 7x/sqrt(7x^2 - 1) * 1/(1 + u^2) = 7x/sqrt(7x^2 - 1)* 1/(1 + 7x^2 - 1) = 7x/sqrt(7x^2 - 1) * 1/7x^2 = 1/(xsqrt(7x^2 - 1))

So that is our final answer. If you have any questions or you're not clear feel free to ask. I also would suggest you read up a bit more on the chain rule.

Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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