Joshua C.

asked • 11d# Calculus Question

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

a.0

b.-1

c.π/6

d.1

## 1 Expert Answer

Doug C. answered • 11d

Math Tutor with Reputation to make difficult concepts understandable

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-x^{2}) ) + cos^{-1}(x) -1/2 (1 - x^{2})^{-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-x^{2}) + x/√(1 - x^{2}) = cos^{-1}(x)

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

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Mark M.

11d