web analytics

Ex 5.7, 6 - Find second order derivatives of ex sin 5x - Finding second order derivatives - Normal form

Slide13.JPG
Slide14.JPG

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
Ask Download

Transcript

Ex 5.7, 6 Find the second order derivatives of the function 𝑒^π‘₯ sin⁑5π‘₯ Let y = 𝑒^π‘₯ sin⁑5π‘₯ Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ . 𝑑𝑦/𝑑π‘₯ = (𝑑(𝑒^π‘₯ " " sin⁑5π‘₯))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 𝑑(𝑒^π‘₯ )/𝑑π‘₯ .sin⁑〖 5π‘₯γ€— + (𝑑(γ€–sin 5〗⁑π‘₯))/𝑑π‘₯ . 𝑒^π‘₯ 𝑑𝑦/𝑑π‘₯ =𝑒^π‘₯ .sin⁑〖 5π‘₯γ€— + cos⁑5π‘₯ (𝑑(5π‘₯))/𝑑π‘₯ . 𝑒^π‘₯ 𝑑𝑦/𝑑π‘₯ = 𝑒^π‘₯. sin⁑〖 5π‘₯γ€— + 5.𝑒^π‘₯. cos⁑5π‘₯ Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯)= (𝑑 (𝑒^π‘₯. sin⁑〖 5π‘₯γ€— " + " 5.𝑒^π‘₯." " cos⁑5π‘₯))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (𝑑 (𝑒^π‘₯. sin⁑〖 5π‘₯γ€—))/𝑑π‘₯ + (𝑑 (5.𝑒^π‘₯." " cos⁑5π‘₯))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (𝑑 (𝑒^π‘₯ sin⁑5π‘₯))/𝑑π‘₯ + 5 (𝑑(𝑒^π‘₯." " cos⁑5π‘₯))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = ((𝑑 (𝑒^π‘₯))/𝑑π‘₯.sin⁑5π‘₯+(𝑑 (sin⁑5π‘₯))/𝑑π‘₯ .𝑒^π‘₯ ) + 5 ((𝑑(𝑒^π‘₯))/𝑑π‘₯ .cos⁑5π‘₯+(𝑑(cos⁑5π‘₯))/𝑑π‘₯ .𝑒^π‘₯ ) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (𝑒^π‘₯.sin⁑5π‘₯+(cos⁑5π‘₯ ) .(𝑑(⁑5π‘₯))/𝑑π‘₯.𝑒^π‘₯ ) + 5 (𝑒^π‘₯.cos⁑5π‘₯+(βˆ’sin⁑〖5 π‘₯)γ€—.(𝑑(⁑5π‘₯))/𝑑π‘₯.𝑒^π‘₯ ) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (𝑒^π‘₯ sin⁑5π‘₯+cos⁑5π‘₯.5.𝑒^π‘₯ ) + 5 (𝑒^π‘₯ cos⁑5π‘₯βˆ’sin⁑〖5 π‘₯γ€—.5.𝑒^π‘₯ ) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 𝑒^π‘₯ sin⁑5π‘₯+5𝑒^π‘₯ cos⁑5π‘₯+5𝑒^π‘₯ cos⁑5π‘₯βˆ’25𝑒^π‘₯ sin⁑〖5 π‘₯γ€— (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 10 𝑒^π‘₯ cos⁑5π‘₯ βˆ’ 24 𝑒^π‘₯ sin⁑〖5 π‘₯γ€— (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) = 2𝒆^𝒙 (πŸ“π’„π’π’”β‘πŸ“π’™ βˆ’ 1𝟐 π’”π’Šπ’β‘γ€–πŸ“ 𝒙〗)

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail