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Example 45 (i) - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 16, 2023 by Teachoo
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Example 42 Important Deleted for CBSE Board 2023 Exams
Example 43 Deleted for CBSE Board 2023 Exams
Example 44 (i)
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Example 45 (i) You are here
Example 45 (ii) Important
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Transcript
Example 45 (Method 1) Differentiate the following π€.π.π‘. π₯. (i) cos^(β1) (sinβ‘π₯) Let π(π₯) = cos^(β1) (sinβ‘π₯) π(π₯) = cos^(β1) (γcos γβ‘(π/2 βπ₯) ) π(π) = π /π βπ Differentiating π€.π.π‘.π₯ πβ(π₯) = (π (π/2))/ππ₯ β (π(π₯))/ππ₯ πβ(π₯) = 0 β 1 πβ(π) = β 1 (π΄π γ π ππ π γβ‘γ=γπππ γβ‘γ(π/2 βπ₯)γ γ ) ("As " (π(π₯))/ππ₯ " = 1 & " π/2 " is constant" ) Example 45 (Method 2) Differentiate the following π€.π.π‘. π₯. (i) cos^(β1) (sinβ‘π₯) Let π(π₯) = cos^(β1) (sinβ‘π₯) Differentiating π€.π.π‘.π₯ πβ²(π₯) = (β1)/β(1 β γ(sinβ‘π₯)γ^2 ) Γ (sinβ‘π₯ )^β² πβ²(π₯) = (β1)/β(1 β sin^2β‘π₯ ) Γcosβ‘π₯ πβ²(π₯) = (β1)/β(cos^2β‘π₯ ) Γcosβ‘π₯ πβ²(π₯) = (β1)/cosβ‘π₯ Γcosβ‘π₯ πβ(π) = β1
