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Example 39 (i) - Chapter 5 Class 12 Continuity and Differentiability
Last updated at December 16, 2024 by Teachoo
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Chapter 5 Class 12 Continuity and Differentiability
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Example 39 Differentiate w.r.t. x, the following function: (i) ā(3š„+2) + 1/ā(2š„^2+ 4) Let y = ā(3š„+2) + 1/ā(2š„^2+ 4 ) Differentiating š¤.š.š”.š„ šš¦/šš„ = š(ā(3š„ + 2) " + " 1/ā(2š„^2 + 4 ))/šš„ šš¦/šš„ = š(ā(3š„ + 2))/šš„ + š(1/ā(2š„^2 + 4 ))/šš„ šš¦/šš„ = š(ā(3š„ + 2))/šš„ + (š(2š„^2 + 4)^((ā1)/2))/šš„ Calculating š(ā(3š„ + 2))/šš„ & (š(2š„^2 + 4)^((ā1)/2))/šš„ separately Calculating š(ā(šš± + š))/š š š(ā(3š„ + 2))/šš„ = 1/(2ā(3š„ + 2 )) Ć š(3š„ + 2)/šš„ = 1/(2ā(3š„ + 2 )) Ć (3+0) = š/(šā(šš + š )) Calculating (š (šš^š + š)^((āš)/š))/š š (š(2š„^2 + 4)^((ā1)/2))/šš„ = (ā1)/2 ć(2š„^2+4)ć^((ā1)/( 2) ā1) . š(2š„^2+ 4)/šš„ = (ā1)/2 (2š„^2+ 4)^((ā3)/( 2)) . (š(2š„^2 )/šš„ + š(4)/šš„) = (ā1)/2 (2š„^2+ 4)^((ā3)/( 2)) . (4š„+0) = (ā4š„)/2 (2š„^2+ 4)^((ā3)/( 2)) = (āšš)/(šš^š+ š)^(š/š) Hence, šš¦/šš„ = š(ā(3š„+2))/šš„ + š(1/ā(2š„^2+ 4 ))/šš„ š š/š š = š/(šā(šš + š )) ā šš/(šš^š+ š)^(š/( š))
