Y=log_xsinx² + (sinx²)^log_ex 

let z =  log_xsinx² 

z = (log sinx²)/(logx)    

now differentiate wrt x

let A = (sinx²)^logx 

log A = (log x) log(sinx²) 

now differentiate wrt x

differentiate this respect to x and divide the upper derivative by the lower one and u get the answer