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Question

Find dydxif y=tan1(5x+13x6x2)

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Solution

ddx(tan15x+13x6x2)Applyingchainruleddxf(u)=dfdududxLetu=5x+13x6x2=ddutan1uddx(5x+13x6x2)Weknowthatddutan1u=1u2+1Step1:ddutan1u=1u2+1Step2:ddx(5x+13x6x2)=(5x+1)(3x6x2)ddx(3x6x2)(5x+1)(3x6x2)2=5(3x6x2)(12x1)(5x+1)(3x6x2)2=30x2+12x+16(3x6x2)2Thereforeddx(5x+13x6x2)=30x2+12x+16(3x6x2)2(Usingquotientruleofdifferentiation)Combiningstep1andstep2:ddutan1u=1u2+1andddx(5x+13x6x2)=30x2+12x+16(3x6x2)2=1[5x+13x6x2]2+130x2+12x+16(3x6x2)2=15x2+6x+818x4+6x3+5x2+2x+5Henceddx(tan15x+13x6x2)=15x2+6x+818x4+6x3+5x2+2x+5

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