derivatives with arcs

Question

Answer 1

r(x) = (x^7)(arcsin(x))

to find r'(x) use the product rule

r'(x) = derivative of 1st term times 2nd term + derivative of 2nd term times 1st term

r'(x) = (x^7)'(arcsin(x)) + (arcsin(x))'(x^7) = (7x^6)arcsin(x) + (x^7)(arcsin(x))'

= 7x^6(arcsin(x) = (x^7)/sqr(1-x^2)

Answer 2

You need to know 2 things:

Derivative of arcsin is 1/sqrt(1-x²)

and use the product rule.

Answer 3

derivaretive of arcsin x is (1 - x²)^-1/2

Use this in the Product Rule