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- Find derivatives of the functions defined as follows. y=-4e-0.3xConsider the curve given by y = 2+ xy. (b) Find all points (x, y) on the curve where the line tangent to the curve has slope . (c) Show that there are no points (x, y) on the curve where the line tangent to the curve is horizontał. (d) Let x and y be functions of time t that are related by the equation y? = 2 + xy. At time i = 5, the dy : 6. Find the value of at time i = 5. dt dx dt value of y is 3 andFind the equation of the curve whose slope at any point is equal to 1+y/(x lnx )-1/lnx and which passes through the point (e,e+1)
- The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)IF THE CURVE OF THE FUNCTION F (X) = Y PASSES THROUGH THE TWO POINTS (2,2) AND (1, K) AND SATISFIES THE EQUATION, WHAT IS THE VALUE OF K? Хау/dx+3у-21) Find an equation of the tangent line to the curve y5+x2y3 = 1+x4y at the point (1,1). 2) Find the slope(s) of the line(s) tangent to the graph x2y+xy2 = 6 at the point(s) where y = 2