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Suppose z = x2 sin y, x = -5s2 + 2t2, y = -10st. Use the chain rule to find and as functions of x, y, s and t. = -20xssiny - 10tx^2cosy = 8xtsiny-10sx^2cosy Find the numerical values of and when (s, t) = (3, 4). (3, 4) = 2704.50 (3, 4) = 2895.27 Suppose w = x/y + y/z, where x = et, y = 2 + sin (2t), and z = 2 + cos (5t). Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite et as x. dw/dt = exp(t)/y + 2cos(2t)/z - 2xcos(2t) + 5ysin(5t)/z^2 Note: You may want to use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y" Use part A to evaluate dw/dt when t = 0. 1/y - 2/z - 2x/y^2
Show transcribed image text Suppose z = x2 sin y, x = -5s2 + 2t2, y = -10st. Use the chain rule to find and as functions of x, y, s and t. = -20xssiny - 10tx^2cosy = 8xtsiny-10sx^2cosy Find the numerical values of and when (s, t) = (3, 4). (3, 4) = 2704.50 (3, 4) = 2895.27 Suppose w = x/y + y/z, where x = et, y = 2 + sin (2t), and z = 2 + cos (5t). Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite et as x. dw/dt = exp(t)/y + 2cos(2t)/z - 2xcos(2t) + 5ysin(5t)/z^2 Note: You may want to use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y" Use part A to evaluate dw/dt when t = 0. 1/y - 2/z - 2x/y^2