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Finding second order derivatives - Normal form
Finding second order derivatives - Normal form
Last updated at May 29, 2023 by Teachoo
Ex 5.7, 2 Find the second order derivatives of the function π₯^20 Let y = π₯^20 Differentiating π€.π.π‘.π₯ ππ¦/ππ₯ = (π(π₯^20))/ππ₯ ππ¦/ππ₯ = γ20π₯γ^(20β1) ππ¦/ππ₯ = γ20π₯γ^19 Again Differentiating π€.π.π‘.π₯ π/ππ₯ (ππ¦/ππ₯) = (π (γ20π₯γ^19))/ππ₯ (π^2 π¦)/(ππ₯^2 ) = (20 π(π₯^19))/ππ₯ (π^2 π¦)/(ππ₯^2 ) = 20 Γ 19 π₯^(19β1) (π^2 π¦)/(ππ₯^2 ) = 20 Γ 19 π₯^18 (π^2 π¦)/(ππ₯^2 ) = 380 π₯^18 Thus, (π ^π π)/(π π^π ) = 380 π^ππ