Finding derivative of Implicit functions

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

Introducing your new favourite teacher - Teachoo Black, at only βΉ83 per month

### Transcript

Ex 5.3, 6 Find ππ¦/ππ₯ in, π₯3 + π₯2π¦ + π₯π¦2 + π¦3 = 81 π₯3 + π₯2π¦ + π₯π¦2 + π¦3 = 81 Differentiating both sides π€.π.π‘.π₯ . π(π₯3 + π₯2π¦ + π₯π¦2 + π¦3)/ππ₯ = (π (81))/ππ₯ π(π₯3)/ππ₯ + π(π₯2π¦)/ππ₯ + (π(π₯π¦2))/ππ₯ + π(π¦3)/ππ₯ =0 3π₯^(3β1) + (π(π₯2π¦))/ππ₯ + (π(π₯π¦2))/ππ₯ + π(π¦3)/ππ₯ Γ ππ¦/ππ¦ = 0 3π₯^2 + (π(π₯2π¦))/ππ₯ + (π(π₯π¦2))/ππ₯ + π(π¦3)/ππ₯ Γ ππ¦/ππ₯ = 0 3π₯^2+ (π(π₯2π¦))/ππ₯ + (π(π₯π¦2))/ππ₯ +3π¦^(3β1) . ππ¦/ππ₯ = 0 3π₯2 + (π(π₯2π¦))/ππ₯ + (π(π₯π¦2))/ππ₯ +3π¦^2 ππ¦/ππ₯ = 0 Using product rule in π₯2π¦ & π₯π¦2 (uv)β = uβv + vβu 3π₯2 + ((π(π₯2))/ππ₯.π¦+π₯2 .(π(π¦))/ππ₯)+((π(π₯))/ππ₯.π¦2+ .(π(π¦2))/ππ₯ π₯ )+ 3y2 ππ¦/( ππ₯) = 0 3π₯2 + (2π₯.π¦+π₯2 (π(π¦))/ππ₯) + (1.π¦2+π₯ .(π(π¦2))/ππ₯ )+ 3y2 ππ¦/( ππ₯) = 0 3π₯2 + (2π₯.π¦+π₯2 (π(π¦))/ππ₯) + (π¦2+π₯ .(π(π¦2))/ππ₯ Γ ππ¦/ππ¦)+ 3y2 ππ¦/( ππ₯) = 0 3π₯2 + 2π₯π¦+π₯2 ππ¦/ππ₯+π¦2+π₯.(π(π¦2))/ππ¦ Γππ¦/ππ₯+3π¦2 ππ¦/( ππ₯) = 0 3π₯2 + 2π₯π¦+π₯2 ππ¦/ππ₯+π¦2 + π₯. 2π¦^(2β1) (ππ¦/ππ₯)+3π¦2 ππ¦/ππ₯=0 3π₯2 + 2π₯π¦+π¦2 + x2 ππ¦/ππ₯+π₯.2π¦ ππ¦/ππ₯+3π¦2 ππ¦/ππ₯=0 "(3" π₯"2 "+" " 2π₯π¦+π¦2")" + ππ¦/ππ₯ (π₯2+2π₯π¦+3π¦2)=0 ππ¦/ππ₯ (π₯2+2π₯π¦+3π¦2)=β "(3" π₯"2 "+" " 2π₯π¦+π¦2")" ππ/ππ= (β "(" ππ"2 " +" " πππ + ππ")" )/((ππ + πππ + πππ) )