If Xm Yn = (x + Y)m + N, Prove That From Class 12 CBSE ... - Zigya

We are given,If xm yn = (x + y)m + nTaking log on both sides, we getlog xm yn = log(x + y)m + nlog xm + log yn = m+n log(x + y)m logx + n logy = m+n log (x+y)

Differentiating above equation w.r.t. x, we get

 straight m over straight x space plus straight n over straight y dy over dx space equals space fraction numerator left parenthesis straight m plus straight n right parenthesis over denominator left parenthesis straight x plus straight y right parenthesis end fraction space space straight x space open parentheses 1 plus dy over dx space close parentheses straight n over straight y dy over dx minus open parentheses fraction numerator straight m plus straight n over denominator straight x plus straight y end fraction close parentheses dy over dx space equals space open parentheses fraction numerator straight m plus straight n over denominator straight x plus straight y end fraction close parentheses minus straight m over straight x open parentheses straight n over straight y minus fraction numerator straight m plus straight n over denominator straight x plus straight y end fraction close parentheses dy over dx space equals space fraction numerator straight x left parenthesis straight m plus straight n right parenthesis minus straight m left parenthesis straight x plus straight y right parenthesis over denominator straight x left parenthesis straight x plus straight y right parenthesis end fraction open parentheses fraction numerator nx plus ny minus my minus ny over denominator straight y left parenthesis straight x plus straight y right parenthesis end fraction close parentheses dy over dx space equals space fraction numerator xm plus xn minus mx space minus my over denominator straight x space left parenthesis straight x plus straight y right parenthesis end fraction dy over dx space equals space straight y over straight x space straight x fraction numerator left parenthesis xn minus my right parenthesis over denominator left parenthesis xn minus my right parenthesis end fraction rightwards double arrow space dy over dx space equals space straight y over straight x And fraction numerator begin display style space straight d squared straight y end style over denominator dx squared end fraction space equals space fraction numerator straight x begin display style dy over dx end style minus straight y over denominator straight x squared end fraction space equals space fraction numerator straight x begin display style straight y over straight x end style minus straight y over denominator straight x squared end fraction space equals space 0

Từ khóa » (xm-yn)2