Calculus Question

Question

If f(x) = xcos^-1(x)-(1-x²)^1/2 find f '(√(3)/2)

a.0

b.-1

c.π/6

d.1

Answer 1

To find f'(x) use the product rule for the 1st term and power-rule/chain-rule for 2nd term,

f'(x) = x (-1)/(√(1-x²) ) + cos^-1(x) -1/2 (1 - x²)^-1/2 (-2x)

To find f'(x) at √3/2 we could substitute right now, but chances are the formula for f'(x) will simplify significantly.

f'(x) = cos^-1(x) - x/√(1-x²) + x/√(1 - x²) = cos^-1(x)

So f'(√3/2) = cos^-1(√3/2) = ?? (what angle has a cos of √3/2?)