Let y = (2x + 3 sin(x))4. Find f (x) and g(x) so that y = f(g(x)) and compute the derivative using the Chain Rule. (Use symbolic notation and fractions where needed.) M = Calculate g 2 if f(u) = 5:8, 11(2) = -5, and \"*(2) = -5. (Give your answer as a whole or exact number.) dx Compute the derivative of the function y using derivative rules. 4 3 y = (12x + 5) (Express numbers in exact form. Use symbolic notation and fractions where needed.) 133x3(l2x4 +5)2 Incorrect Use the General Power Rule to compute the derivative. 2 5 y = (4 5x 6x ) (Use symbolic notation and fractions where needed.) Compute the derivative of the function y using derivative rules. y = 1K9 + 6x + sin(x) (Express numbers in exact form. Use symbolic notation and fractions where needed.) Use the Chain Rule to find the derivative. (Use symbolic notation and fractions where needed.) d (sin (5x)) 13 dxUse the Chain Rule to find the derivative. (Use symbolic notation and fractions where needed.) (x2 + 1 1x + 1) -112 =Use the Chain Rule to nd the derivative. y = 211] (Use symbolic notation and fractions where needed.) Use the Chain Rule to nd the derivative. y = e545 (Use symbolic notation and fractions where needed.) Use the Chain Rule to nd the derivative. y = cos9 (e49) (Express numbers in exact form. Use symbolic notation and fractions where needed.) d6 Calculate the following derivative. (Use symbolic notation and fractions where needed.) m3)\"2 x+21 Find the derivative of y(x) = using the appropriate rule or combination of rules. (Use symbolic notation and fractions where needed.) Find the derivative using the appropriate rule or combination of rules. cos (3) 8+x2 me) = (Use symbolic notation and fractions where needed.) Find the derivative using the appropriate rule or combination of rules. y = (kx + (3195 where k and b are any constants. (Use symbolic notation and fractions where needed.) \fAn expanding sphere has radius r = 0.8: cm at time t (in seconds). Let Vbe the sphere's volume. Find % when r = 6 and t = 10. (Use symbolic notation and fractions where needed.) E d! = ll: CID/s r=6 dt = \\\\ arm's I=10 A 2005 study by the Fisheries Research Services in Aberdeen, Scotland, suggests that the average length of the species Clupea harengus (Atlantic herring) as a function of age t (in years) can be modeled by L(t) = 32 (1 - e-0.371 ) cm for 0 S t - 13. L (cm) 32 4 30- 20+ 10- 6 8 10 12 t (year) How fast is the length changing at age t = 10 years? (Use e = 2.72. Give your answer to two decimal places.) rate of change of length = cm/yr At what age A is the length changing at a rate of 4 cm/yr? (Use e = 2.72. Give your answer to two decimal places.) A = yearsUse the table of values to calculate the derivative of the function at the given point. 1 6 f(x) 4 0 7 f'(x) 5 7 5 g(x) 4 1 6 g'(x) 5 1 4 (Give your answer as a whole number.) d Emu