AboutScotto 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.
Question 1. If A and B are constants, show that the derivative with respect to x of each of the following functions
2sin^-1 [(x-B)/(A-B)]^1/2 and 2tan^-1 [(x-B)/(A-x)]^1/2 is [(A-x)(x-B)]^-1/2
Answer I'll assume in both cases that the exponet is done before the trig funtion. If not, let me know.
The derivative d(sin^-1(u(x)))/dx, is equal to
(1/squareroot(1-u²))du/dx.
Here, u(x) = [(x-B)/(A-B)]^(1/2) so
du/dx = (1/2)[(x-A)/(A-B)]^(-1/2)[1/(A-B)].
The derivative d{tan^-1[u(x)]}/dx is equal to [1/(1+u²)]du/dx
where u(x)=[(x-B)/(A-x)]^(1/2).
du/dx=(1/2)[(x-B)/(A-x)]^(-1/2)[(A-x)+(x-B)]/(A-x)²].
This can be reduced even farther by combining terms.
