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Example 29 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Example 29 Differentiate the following w.r.t. x: (ii) sin⁑(log⁑π‘₯), π‘₯ > 0Let 𝑦 =sin⁑(log⁑π‘₯) Differentiating both sides 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(sin⁑(log⁑π‘₯)) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = cos⁑(log⁑π‘₯) . (𝑑⁑(log⁑π‘₯ ) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = cos⁑(log⁑π‘₯) . 1/π‘₯ π’…π’š/𝒅𝒙 = (𝒄𝒐𝒔⁑(π’π’π’ˆβ‘π’™)" " )/𝒙 (𝑠𝑖𝑛⁑π‘₯ )^β€²=π‘π‘œπ‘ β‘π‘₯ ((π‘™π‘œπ‘”β‘π‘₯ )^β€²= 1/π‘₯)

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