![]() However the x and y coordinates are swapped so the gradient for the inverse according differentiation by first principles is => d/dx f^-1(4) = (pi/2)^-1 = 2/pi since the coordinates of x and y are swapped. ![]() ![]() Using f'(x) substituting x=0 yields pi/2 as the gradient. So you choose evaluate the expression using inverse or non-inverse function So the coordinate for the inverse function is (4, 0) and the non-inverse function (0, 4) By inspection x = 0 satisfies the equation.Īlternatively substitute x=4 for the inverse function then find the y-coordinate. So now the x-coordinate needs to be found for f(x)=4. So the x-coordinate for the inverse is 4 however the coordinate is swapped. The key thing to note is the coordinates of x and y are swapped for the inverse. Now the question is at what point should the derivative be evaluated. So the goal is to evaluate d/dx(f^-1(x)) at x=4.
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