help me solve these problems I have attached the answers for these problems

7. Find the derivatives. a. f(x) = 2x57cos(x) b. y=3x2tan(x) sec(x) c. g(x)= 3 d. h(x)=cot(4x) x 7 e. f(x)=(3x5+8)6 f. g(x)=3x2cos(6x3) 3 g. h(x)=sin4(2x5) h. 5:129r . 3 2 8 . x32x+3 I. yZXs-l--l--lXz-ls J. f(X)=W k (X): 2X3 8 l =4Q/xis+ 3 +8x+5 ' g 5x2+3 ' Y J? m. f(x)='2X+3 n. y:$/sin5(3x2) x3+1 8. A heat probe is attached to the heat exchanger of a heating system. The temperature T (Celsius) is recorded t seconds after the furnace is started. The function T(t) = m can 58+t be used to model the temperature for the first 2 minutes. a. Find the average rate of change in temperature fort = 20 and t = 60. b. Find the instantaneous rate of change in temperature for t = 15. 9. Find the equation of the tangent line to f( X) = ln(3X 1) at X = %. 10. Find :y for each equation implicitly. X 6x+7y 3 =3x a. x+7xy=8 b. tan2(y)=8x+'lO c. 8y 11. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 12811 cubic inches. At what rate is the length h changing when the radius r is 1.8 inches? (Hint: V = nrzh) 12. The formula for the volume of a tank V = m3 where ris the radius of the tank. If water is flowing in at the rate of 15 cubic feet per minute, find the rate at which the radius is changing when the radius is 3 feet. 13. Two boats leave the same port at the same time with one boat traveling north at 15 knots per hour and the other boat traveling west at 12 knots per hour. How fast is the distance between the two boats changing after 2 hours? 14. A 5-meter-long ladder is leaning against the side of a house. The foot of the ladder is pulled away from the house at a rate of 0.4mlsec. Determine how fast the top of the ladder is descending when the foot of the ladder is 3 meters from the house. 7. a. f'(x) = 10x4 + 7 sin(x) b. dy = 6x tan(x) + 3x2 sec2(x) dx C. g'(x) = (X -7) sec(x) tan(x) - 3x2 sec(x) d. h'(x) = -4csc2(4x) ( x 3 - 7 ) 2 e. f'(x) = 6(3x5 +8)515x4 f. g'(x) = 6xcos(6x3) - 3x2[18x2 sin(6x3) ] g. h'(x) = 4 sin3(2x5) cos(2x5)10x4 h. ds - = et(3+3 + 1) dt