If anyone could help me with these questions, please do so! Also please provide detailed solutions and to write down solutions on paper. Thank you!

1. Find the derivative for g(x) = (x2 + 1)(3x4 - 2x3) a) by expanding first, then simplifying and finding the derivative of each term (ie. without using the Product Rule) b) by using the Product Rule Note : Both derivatives should be the same. 2. Find the derivative for each of the following functions. Simplify your final answer. a. g(x) = (2+ 7x) (x -3) b. f (a) = (5202 + 3ac) (203 + 2ac - 1) c. h (x) = (1-22) (1+22) d. y = 2 (sin x) (cos ac) e. f (a) = -23Vx f. k(x) = (723 + x) (3 sin ac) 3. Find the derivative for - m(x) = -ex cos x and then evaluate at x = 0 and at x = 1 (ie. find m'(0) and m'(1)). Make sure that your calculator MODE is set to RADIANS when evaluating the "trigonometric" part of the function. Show both a graphic (Desmos) and algebraic solution. 4. Determine the point(s) where the tangent to the curve is horizontal (the slope of the tangent line is zero (0)) for the function y = (x2+ 2x+1)(x2+ 2x+1)1. Find the derivative of each of the the following functions. Exit Fullscreen Show your work. a f (x) = (3x - 2 2) 4 6 ) h (2 ) = ( 2x2 + 3x - 5 ) 8 c) f (2 ) = (2 - 16) d) f (xc ) = 17+ va e) g (2 ) = - 7x V5-2x f) h (z ) = 4(10* + 2ex + sin (3x))-5 2. From the year 2000, the world's growing population can be modelled by an exponential equation, P(t) = 5.35e0.019t , where t is the number of years past 2000 and P is the number of people in the billions. a. Estimate the world's population after 20 years has passed (ie. 20 years from 2000) b. At what rate is the population changing at this time?3. The height of the tides at a certain spot in Nova Scotia can be found by the equation h(t) = 5sin(0.5t + 2) + 6, where t is the time in hours (using a 24 hour clock) and h is the height in metres. What is the rate of change of height at a time of 07:00 h? 4. An apple orchard now has 60 trees planted per hectare and the average yield is 500 apples per tree. For each additional tree planted per hectare, the average yield per tree is reduced by approximately five apples. How many trees per hectare will give the largest crop of apples? 5. a) Develop a solution for the derivative of y = In x . (Hint : Start your solution with a first step of rewriting the equation in exponential form ( e) = x), take the derivative of both sides, use the chain rule and solve for dy/dx - this method is called "Implicit Differentiation") b) Use the result from a) above to find the f(x) if f(x) = In(x3 ) c) Find y' when given y = x . In(5x)