What is the derivative of F (x) = √ (2x-x ^ 2) I calculated 2 - 2x √ (2x - 2), but I think it must be wrong, because I don't know how to calculate this compound How to find the derivative with radical? Then how to calculate the monotone interval after derivation?

What is the derivative of F (x) = √ (2x-x ^ 2) I calculated 2 - 2x √ (2x - 2), but I think it must be wrong, because I don't know how to calculate this compound How to find the derivative with radical? Then how to calculate the monotone interval after derivation?

Take the root sign as a whole, the derivation of √ x is 1 / (2 √ x), and then multiply by the derivation of the part in the root sign
[1/(2√2x-x^2)] * (2-2x) =(1-x)/√(2x-x^2)
If the derivative is greater than 0, the range of solution is monotone increasing
If the derivative is less than 0, the range of solution is monotone decreasing interval