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About Scotto
Expertise
Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.

Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

You are here: Experts > Teens > Homework/Study Tips > Calculus > Calculus Early Vectors Section 4.4

Topic: Calculus

Expert: Scotto
Date: 6/13/2008
Subject: Calculus Early Vectors Section 4.4

Question
Hi i need some help with this one question i have to find f' and state the domains of f and f'

the question is F(X)= cos(ln x)

Answer
The derivative is the chain rule. You have f(g(x)), so the derivative is f'(g(x))g'(x) where f(x)=cos(x) and g(x)=ln(x).
The derivative of cos(x) is -sin(x) and the derivative of ln(x) is 1/x. All you've got to do is put the g(x) in for x in -sin(x) and multilpy that by 1/x.

The domain is the same as the domain for ln(x) (all positve x) and
the range is -1<=x<=1.

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