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Ex 5.7, 2 Class 12 Maths - Find second order derivative of x^20

Ex 5.7, 2 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Ex 5.7, 2 Find the second order derivatives of the function π‘₯^20 Let y = π‘₯^20 Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(π‘₯^20))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = γ€–20π‘₯γ€—^(20βˆ’1) 𝑑𝑦/𝑑π‘₯ = γ€–20π‘₯γ€—^19 Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯) = (𝑑 (γ€–20π‘₯γ€—^19))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (20 𝑑(π‘₯^19))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 20 Γ— 19 π‘₯^(19βˆ’1) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 20 Γ— 19 π‘₯^18 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 380 π‘₯^18 Thus, (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) = 380 𝒙^πŸπŸ–

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