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Example 23 - Differentiate sin (cos (x^2)) - Teachoo - Examples

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Example 23 Differentiate sin ⁑(cos ⁑(π‘₯2)) with respect to π‘₯ .Let 𝑦 = " " sin ⁑(cos ⁑π‘₯2) We need to find derivative of 𝑦 𝑀.π‘Ÿ.𝑑.π‘₯ i.e. 𝑦^β€² = (𝑠𝑖𝑛⁑〖 (cos⁑〖π‘₯^2 γ€— )γ€— ) 𝑑𝑦/𝑑π‘₯ = 𝑑(𝑠𝑖𝑛⁑〖 (cos⁑〖π‘₯^2 γ€— )γ€— )/𝑑π‘₯ = cos (cos⁑〖π‘₯^2 γ€— ) . 𝑑(cos⁑〖π‘₯^2 γ€— )/𝑑π‘₯ = cos (cos⁑〖π‘₯^2 γ€— ). (βˆ’sin⁑〖π‘₯^2 γ€— ) . 𝑑(π‘₯^2 )/𝑑π‘₯ = cos (cos⁑〖π‘₯^2 γ€— ). (βˆ’sin⁑〖π‘₯^2 γ€— ) . 2π‘₯ = βˆ’ 2x sin 𝒙^𝟐. cos (cos 𝒙^𝟐)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.