can anyone give me the steps to find the derivative of this function y=x^(2-x) using the limit definition? pic unrelated
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.
But perhaps you need a solution without using the known rules (limit definition).