Differentiate w.r.t. x the function `(sinx-cosx)^((sinx-cosx)),pi/4 < x < (3pi)/4`

Explanation

`y = (sinx-cosx)^(sinx-cosx)`

Taking log both sides,

`logy = (sinx-cosx)log(sinx-cosx)`

Now, differentiating both sides,

`1/ydy/dx = log(sinx-cosx)(cosx+sinx)+ (sinx-cosx)*1/(cosx-sinx)*(cosx+sinx)`

`1/ydy/dx = (cosx+sinx)(log(sinx-cosx)+1)`

Putting value of `y`

`dy/dx = (sinx-cosx)^(sinx-cosx) ((cosx+sinx)(log(sinx-cosx)+1))`