Ex 5.3, 9 - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 11, 2021 by Teachoo
Last updated at March 11, 2021 by Teachoo
Transcript
Ex 5.3, 9 Find ππ¦/ππ₯ in, y = sin^(β1) (2π₯/( 1 + 2π₯2 )) π¦ = sin^(β1) (2π₯/( 1 + 2π₯2 )) Putting x = tan ΞΈ π¦ = sin^(β1) (2π₯/( 1 + π₯2 )) π¦ = sin^(β1) ((2 π‘ππβ‘π)/(1 + γπ‘ππγ^2 π)) π¦ = sin^(β1) ( sinβ‘2ΞΈ) π¦ = 2π Putting value of ΞΈ = γπ‘ππγ^(β1) π₯ π¦ = 2 γπ‘ππγ^(β1) π₯ ("Since " π ππβ‘2π" = " (2 π‘ππβ‘π)/(1 + γπ‘ππγ^2 π)) Since x = tan ΞΈ β΄ γπ‘ππγ^(β1) x = ΞΈ Differentiating both sides π€.π.π‘.π₯ . (π(π¦))/ππ₯ = (π (2 γπ‘ππγ^(β1) π₯" ) " )/ππ₯ ππ¦/ππ₯ = 2 (π (γπ‘ππγ^(β1) π₯" ) " )/ππ₯ ππ¦/ππ₯ = 2 (1/(1+ π₯^2 )) π π/π π = π/(π+γ πγ^π ) ((γπ‘ππγ^(β1) π₯")β = " 1/(1 + π₯^2 ))
Finding derivative of Inverse trigonometric functions
Example 26 Important
Example 27
Derivative of cot-1 x (cot inverse x)
Derivative of sec-1 x (Sec inverse x)
Derivative of cosec-1 x (Cosec inverse x)
Ex 5.3, 14
Ex 5.3, 9 Important You are here
Ex 5.3, 13 Important
Ex 5.3, 12 Important
Ex 5.3, 11 Important
Ex 5.3, 10 Important
Ex 5.3, 15 Important
Misc 5 Important
Misc 4
Misc 13 Important
Finding derivative of Inverse trigonometric functions
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