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Find dy/dx and d 2 y/dx 2. x = e t, y = te −t. For which values of t is the curve concave upward? (Enter your answer using interval notation.)
Find dy/dx and d 2 y/dx 2. x = e t, y = te-t. Solution: x = e t. dx/dt = de t /dt = e t. dy/dt = d( te-t)/dt. dy/dt = tde-t /dt + e-t d(t)/dt. dy/dt = -te-t + e-t = (1 - t)e-t. dy/dx = dy/dt/dx/dt = (1 - t)e-t /e t. dy/dx = (1 - t)e-2t ---(1) d²y/dx² = d/dx(dy/dx) Since x = e t and y = te-t. xy = e t × te-t. xy = t. Hence we can write ...
18 lip 2023 · The derivative dy/dx is e−2t(1 - t) and the second derivative d2y/dx2 is [-2e−t(1 - t) - e−2t(1 - t)] / (et)². Explanation: To find dy/dx, we need to use the chain rule. The chain rule states that if y = f(g(t)), then dy/dt = f'(g(t)) * g'(t). In this case, we have y = te−t, so we can rewrite it as y = t * e−t. Using the chain rule ...
Click the 'Go' button to instantly generate the derivative of the input function. The calculator provides detailed step-by-step solutions, facilitating a deeper understanding of the derivative process. implicit\:derivative\:\frac {dy} {dx},\: (x-y)^2=x+y-1.
VIDEO ANSWER: Hi, so we are given X is equals to T minus e to the power T and Y is equals to T plus e to the power minus of T. So we have asked to find dy by dx and d square over dx square. So since we know that dy by dx, this can be equals to d by
4 gru 2016 · Then, dy/dx can be found as (dy/dt)/ (dx/dt), and the second derivative d2y/dx2 can be obtained by differentiating dy/dx with respect to x, which will utilize the quotient rule. Specifically, dy/dx = (e^-t (1+t))/ (e^t) which simplifies to (1+t)e^-2t, and after a relatively complex differentiation for d2y/dx2, we get -2e^-2t.
Find dy/dx . y = int_sqrt[3]x^pi/4 sin (t^3) dt; Find dy/dx: y= \int_0^x \sqrt{1+t^2} dt; Please find dy/dx and d^{2}y/dx^{2} for the curve x = t^{2} - t, y = 2t - 1. Find the indefinite...
