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diffrentiate with respect to x .... (xcosx)^1/x+(xsinx)^x
question is(xcosx)^1/x +(xsinx)^x take (xcosx)^1/x =m logm =1/x *(log(xcosx) differentiate wrt to X 1/m dm/dx =-1/x^2 *(log(xcosx)) + (1/x*xcosx)*(cosx-xsinx) solve and get dm/dx similarly take (xsinx)^x =n logn = x(log(xsinx)) differentiate wrt to X 1/n *(dn/dx) = log(xsinx) + x*(1/Xsinx)*(sinx+xsinx) get dn/dx from above one dm/dx +dn/dx gives the differentiation of given question....... formulaes used are 1)differentiationof logy is 1/y *(dy/dx) 2)differentiation of xsinx is sinx +xcosx 3)differentiation of xcosx is cosx -xsinx
question is(xcosx)^1/x +(xsinx)^x
take (xcosx)^1/x =m
logm =1/x *(log(xcosx)
differentiate wrt to X
1/m dm/dx =-1/x^2 *(log(xcosx)) + (1/x*xcosx)*(cosx-xsinx)
solve and get dm/dx
similarly take (xsinx)^x =n
logn = x(log(xsinx))
1/n *(dn/dx) = log(xsinx) + x*(1/Xsinx)*(sinx+xsinx)
get dn/dx from above one
dm/dx +dn/dx gives the differentiation of given question.......
formulaes used are 1)differentiationof logy is 1/y *(dy/dx)
2)differentiation of xsinx is sinx +xcosx
3)differentiation of xcosx is cosx -xsinx
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