Example 24 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 24 Find the derivative of f given by π (π₯)=γπ ππγ^(β1) π₯ assuming it exists. π (π₯)=γπ ππγ^(β1) π₯ Let π= γπππγ^(βπ) π sinβ‘γπ¦=π₯γ π=π¬π’π§β‘γπ γ Differentiating both sides π€.π.π‘.π₯ ππ₯/ππ₯ = (π (sinβ‘π¦ ))/ππ₯ 1 = (π (sinβ‘π¦ ))/ππ₯ Γ ππ¦/ππ¦ 1 = (π (sinβ‘π¦ ))/ππ¦ Γ ππ¦/ππ₯ 1 = cosβ‘π¦ ππ¦/ππ₯ 1/cosβ‘π¦ =ππ¦/ππ₯ ππ¦/ππ₯ = 1/πππβ‘π ππ¦/ππ₯= 1/β(π β γπππγ^π π) Putting π ππβ‘γπ¦=π₯γ ππ¦/ππ₯= 1/β(1 β π^π ) Hence, (π (γπππγ^(βπ) π" " ))/π π = π/β(π β π^π ) "We know that" γπ ππγ^2 π+γπππ γ^2 π=1 γπππ γ^2 π=1βγπ ππγ^2 π πππβ‘π½=β(πβγπππγ^π π½) " " As π¦ = γπ ππγ^(β1) π₯ So, πππβ‘π = π
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About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo