derivative of f(x) = 47(sqrt{32-x^2})?

Question

cant figure it out for an elasticity problem im trying to solve.

Answer 1

df/dx = d/dx {47 * sqrt(32 - x^2)}
= 47 * d/dx { [32 - x^2]^(1/2) }
= 47* (1/2) * (32-x^2)^(-1/2) * (0-2x)
= [-47 *(1/2) * 2x] / sqrt(32 - x^2)
= (-47x) / [sqrt(32 - x^2)]

Answer 2

f (x) = 47 ( 32 - x ² )^(1/2)
f `(x) = (1/2) ( 47) ( 32 - x ² ) ^(-1/2) (- 2x)
f `(x) = (- 47 x) / ( 32 - x ² )^(1/2)

Answer 3

f(x) = 47(32-x^2)^(1/2)

f'(x) = 47/2(32-x^2)^(-1/2)(-2x)

= (-47x)/sqrt(32-x^2)