Finding second order derivatives- Implicit form

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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### Transcript

Ex 5.7, 11 If y=5 cosβ‘γπ₯β3 sinβ‘π₯ γ ,prove that π2π¦/ππ₯2 + y = 0 y = 5 cosβ‘γπ₯β3 sinβ‘π₯ γ Differentiating π€.π.π‘.π₯ ππ¦/ππ₯ = (π(5 cosβ‘γπ₯β3 sinβ‘π₯ γ))/ππ₯ ππ¦/ππ₯ = (π(5 cosβ‘π₯))/ππ₯ β (π(3 sinβ‘π₯))/ππ₯ ππ¦/ππ₯ = β 5 sinβ‘π₯ β 3 cosβ‘π₯ Again Differentiating π€.π.π‘.π₯ π/ππ₯ (ππ¦/ππ₯) = (π γ(β 5 sinγβ‘π₯ γβ 3cosγβ‘γπ₯)γ)/ππ₯ (π^2 π¦)/(ππ₯^2 ) = β(π(5 sinβ‘π₯))/ππ₯ β (π(3 cosβ‘π₯))/ππ₯ (π^2 π¦)/(ππ₯^2 ) = β 5 cosβ‘π₯ β 3 γ(βsinγβ‘γπ₯)γ (π^2 π¦)/(ππ₯^2 ) = β 5 cosβ‘π₯ + 3 sinβ‘π₯ (π^2 π¦)/(ππ₯^2 ) = β (5 cosβ‘π₯ β 3 sinβ‘π₯) (π^2 π¦)/(ππ₯^2 ) = βy (π^2 π¦)/(ππ₯^2 ) + y = 0 Hence Proved As y = 5 cosβ‘γπ₯β3 sinβ‘π₯ γ