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About Vijilant
Expertise Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.
Experience Teacher of math for 50 years
Organizations ATL
Publications Journal of mathematics and its applications
Education/Credentials BSc Hons Liverpool
Awards and Honors State Scholarship 1955
Past/Present Clients I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things.
One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.
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You are here: Experts > Science > Mathematics > Number Theory > ap calculus ab
Expert: Vijilant - 11/4/2009
Question my problems (set 2):
For Exercises 9 and 10 find the derivative of each expression and simplify.
9. (1/a)((1/b)(x²)-(2/a)(x)-(d/x))
10. (-8x^-8)+(12√x)
Answer Hello Asad
You don't say what to differentiate with respect to, but I shall assume it is x.
9. (1/a)(2x/b - 2/a + d/x^2). It is arguable what the simplest expression is here.
It may be 2x/(ab) - 2/a^2 + d/(ax^2), or an expression with common denominator.
The one I give is best for eg. differentiating again.
10. 64x^(-9) + 6x^(-1/2) = 64/x^9 + 6/√x
Best wishes
vijilant
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