DIFFERENTIATION

Asked by harshitsinghal14012002 | 22nd May, 2022, 07:17: PM

Expert Answer:

straight y equals 1 plus fraction numerator straight p open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses over denominator left parenthesis straight x minus straight p right parenthesis open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses end fraction plus fraction numerator qx left parenthesis straight x minus straight r right parenthesis over denominator left parenthesis straight x minus straight p right parenthesis open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses end fraction plus fraction numerator rx squared over denominator left parenthesis straight x minus straight p right parenthesis open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses end fraction
rightwards double arrow y equals 1 plus fraction numerator 1 over denominator left parenthesis straight x minus straight p right parenthesis open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses end fraction open square brackets straight p open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses plus qx left parenthesis straight x minus straight r right parenthesis plus rx squared close square brackets
rightwards double arrow fraction numerator d y over denominator d x end fraction equals 1 plus fraction numerator 1 over denominator left parenthesis straight x minus straight p right parenthesis open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses end fraction open square brackets straight p open parentheses straight x minus straight q close parentheses plus straight p open parentheses straight x minus straight r close parentheses plus straight q left parenthesis straight x minus straight r right parenthesis plus qx plus 2 rx close square brackets
space space space space space plus open square brackets straight p open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses plus qx left parenthesis straight x minus straight r right parenthesis plus rx squared close square brackets
space space space space space space space space open square brackets fraction numerator 1 over denominator left parenthesis straight x minus straight p right parenthesis end fraction open parentheses fraction numerator 1 over denominator open parentheses straight x minus straight q close parentheses open parentheses straight x minus straight r close parentheses squared end fraction plus fraction numerator 1 over denominator open parentheses straight x minus straight q close parentheses squared open parentheses straight x minus straight r close parentheses end fraction close parentheses plus fraction numerator 1 over denominator left parenthesis straight x minus straight q right parenthesis end fraction open parentheses fraction numerator 1 over denominator open parentheses straight x minus straight p close parentheses open parentheses straight x minus straight r close parentheses squared end fraction plus fraction numerator 1 over denominator open parentheses straight x minus straight p close parentheses squared open parentheses straight x minus straight r close parentheses end fraction close parentheses plus fraction numerator 1 over denominator left parenthesis straight x minus straight r right parenthesis end fraction open parentheses fraction numerator 1 over denominator open parentheses straight x minus straight p close parentheses open parentheses straight x minus straight q close parentheses squared end fraction plus fraction numerator 1 over denominator open parentheses straight x minus straight p close parentheses squared open parentheses straight x minus straight q close parentheses end fraction close parentheses close square brackets

Answered by Renu Varma | 29th May, 2022, 07:07: PM