If y = 5 cos x – 3 sin x, then (d 2 y)/(dx 2 ) is equal to:

(a) −y     (b) y
(c) 25y   (d) 9y

This question is inspired from Ex 5.7, 11 - Chapter 5 Class 12 - Continuity and Differentiability

Slide36.JPG

Slide37.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 14 If y = 5 cos x – 3 sin x, then (𝑑^2 𝑦)/(𝑑π‘₯^2 ) is equal to: (a) βˆ’y (b) y (c) 25y (d) 9y y = 5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€— Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€—))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(5 cos⁑π‘₯))/𝑑π‘₯ βˆ’ (𝑑(3 sin⁑π‘₯))/𝑑π‘₯ π’…π’š/𝒅𝒙 = βˆ’ 5 π’”π’Šπ’β‘π’™ βˆ’ 3 𝒄𝒐𝒔⁑𝒙 Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯) = (𝑑 γ€–(βˆ’ 5 sin〗⁑π‘₯ γ€–βˆ’ 3cos〗⁑〖π‘₯)γ€—)/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’(𝑑(5 sin⁑π‘₯))/𝑑π‘₯ βˆ’ (𝑑(3 cos⁑π‘₯))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ 5 cos⁑π‘₯ βˆ’ 3 γ€–(βˆ’sin〗⁑〖π‘₯)γ€— (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ 5 cos⁑π‘₯ + 3 sin⁑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ (5 𝒄𝒐𝒔⁑𝒙 βˆ’ 3 π’”π’Šπ’β‘π’™) (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) = βˆ’y So, the correct answer is (A)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.