I was doing a long exercise when come to this point: calculate the inverse function of y=2x+sinx(x∈R) and its derivative. I know that the derivative of an inverse function is 1/f′(x) but it is not enough as x=f−1(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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