Example 27 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 8, 2019 by Teachoo
Transcript
Example 27 Find the derivative of f given by f (x) = tanβ1 π₯ assuming it exists. f (x) = tanβ1 π₯ Let y = tanβ1 π₯ tanβ‘π¦ = π₯ β΄ π₯ = tanβ‘π¦ Differentiating both sides π€.π.π‘.π₯ (π(π₯))/ππ₯ = (π (tanβ‘π¦ ))/ππ₯ 1 = (π (tanβ‘π¦ ))/ππ₯ We need dπ¦ in denominator, so multiplying & Dividing by ππ¦. 1 = (π (tanβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = γπ¬ππγ^π π . ππ¦/ππ₯ 1 = (π + πππππ) ππ¦/ππ₯ ππ¦/ππ₯ = 1/(1 + γπππ§γ^πβ‘π ) Putting π‘ππβ‘π¦ = π₯ ππ¦/ππ₯ = 1/(1 + π^π ) As π¦ = tan^(β1) π₯ So, tanβ‘π¦ = π₯ Hence (π (γπππ§γ^(βπ)β‘γπ)γ)/π π = π/(π + π^π )
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.