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Step 4 of 5 Evaluate d (3x y), using the methods of implicit differentiation and recognizing that it is a product of the dx expressions 3x and y. -(3x y) = 3x3 d (y) (3x 3 ) dx dx dx dy = + dx1B. [13 Points] OSCALC1 3.9.350. An isotope of an element has a ha IHife of approximately 18 hours. Initially there are 15 grams of the isotope present. (3) Write the exponential function, Q[t}, that relates the amount of substance remaining as a function oft, measured in hours. QU) = (b) Use part {a} to determine the rate at which the substance is decaying in t hours. Q'U'} = (c) Use part (b) to determine the late of decay (in glhr) at t = 6 hours. (Round your answer to four decimai places.) |:| gfhr 19. [12 Points] OSCALC1 3.9.352. loo - rm % The relative rate ofchange of a differentiable function y = x) is given by H ) x *CX b ' e where a, b, and c are constants. One model for population growth is a Gomperiz growth function, given by P(x) = ee (3) Find the relative rate of change formula for the generic Gomperiz function. (b) Use part {a} to nd the relative rate of change ofa popuiation in x : 20 months when a : 202, b : 0.0198, and c : 0.13. (Round your answer to five decimal places.) :I% Step 2 of 4 In the given problem, we implicitly differentiate by taking the derivative with respect to x of both sides of the equation. d (y) d dx dx (5 cos (x + y)) Evaluate the derivative with respect to x of the left-hand side of the equation, y. d (y) = dy dx X dx\f8. [0/2 Points] DETAILS PREVIOUS ANSWERS OSCALC1 3.8.322. Find y' and y" for x- + 4xy - 9y