Thursday, October 31, 2019

derivatives - Inverse function of y=2x+sinx


I was doing a long exercise when come to this point: calculate the inverse function of y=2x+sinx(xR) and its derivative. I know that the derivative of an inverse function is 1/f(x) but it is not enough as x=f1(y). So I tried to find the inverse function but I'm completely stuck just in this point. Can somebody help me please? Thanks in advance for your help!!


Answer



Hint: write x=2y+sin(y), then 1=2y+cos(y)y, hence y=1/(2+cos(y)), that will be the derivative of the inverse. If you can solve that differential equation you'll have the inverse ...


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