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Differentiating inverse trigonometric functions Find the derivative of f(x) = arcsin (4x2) NOTE: Remember that arcsin (x), arccos() and arctan(a) are alternative notations for the inverse trigonometric functions sin (a), cos (a) and tan (x). f' (2 ) = 1Using the chain rule Find the derivative of f(x) = e -2x2-3 f' (a) = 1Motion of on object in IRS Suppose the position of an object at time t is given by x(t) = (5 cos(3 t), 5 sin(3t), 3t). What is the velocity vector of the object at time t? v(t) =Using the chain rule Find the derivative of the function Mar) 2 (5 1205(3) 1)2 35(3) =|_ L'Hopital's rule Evaluate sin? (a) lim x->0 3 cos(x) - 3 sin (x) lim = 7-0 3 cos (x) - 3