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derivative
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can anyone give me the steps to find the derivative of this function y=x^(2-x) using the limit definition? pic unrelated
>>
y=2x-x^2
(h->0)lim(2(x+h)-(x+h)^2 - 2x + x^2)/h
=lim(2h - 2xh - h^2)/h
=lim(2 - 2x - h) = 2 - 2x

if you use y' = f'(x) = (h->0)lim(f(x+h) - f(x))/h
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>>40716
y = exp((2-x)lnx)
so it will not be as easy
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>>40681
It's easier to write the function differently first:
x^(2-x) = e^ln(x^(2-x)) = e^((2-x)ln x)

Now you should be able to solve it using the derivatives of the exponential function and of the natural logarithm, the chain rule, and the product rule.

https://en.wikipedia.org/wiki/Derivative#Rules_of_computation

But perhaps you need a solution without using the known rules (limit definition).