Correct Answer - `(i) (1)/(xlog x ) " "(ii) secx " "(iii) 3e^(3x) " "(iv) 2x sin (cot x^(2) ) cosec^(2)x^(2)" "(v) -4(e^(x) -e^(-x))" "(vi) (2sin x )/((1+cos x)^(2))`
माना ` log x ^(2) =t " "rArr (1)/(x^(2))* 2x dx = dt rArr (2)/(x ) dx =dt (d)/(dx) (log log x ^(2)) =(d)/(dt)(log t ) (dt)/(dx) =(d)/(dt) =(d)/(dt) (log t ) (2)/(x) `
` " "= (1)/(t)* (2)/(x) =(2) /(x log x ) =(2) /(x*log x^(2))=(1)/(xlog x )`
