If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

9Screen Recording 2023-12-02 at 2.43.56 AM

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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2nd way: integral ∫ log √x(x^n) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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2 ways: ∫ 1/(10x^2 -x-21) dx

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COMMON MISTAKE!: exp derivative d/dx(a^x) ≠ x a^(x-1)

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Review: trig tan(x+360)= tan(x) & tan(x+180)=tan(x)

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COMMON MISTAKE!: directive d/dx(sin(x) cos(x)) ≠ d/dx(sin(x)) d/dx(cos(x))

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2nd/2 ways: ∫2/(x^2-x-6) dx

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Alternate way: ∫1/(x^2+a^2) dx

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#16 MIT 2022 Integration Bee Qualifying Exam

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count show Σak+b = aΣk + nb where k=1 to n

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Review: trig sin(x+180)= -sin(x) & cos(x+180)=-cos(x)

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Find 1) E(X) 2) E(3X) 3) E(3x+2)

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#14 MIT 2022 Integration Bee Qualifying Exam

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trig integral Find cos^2(x) sin(x) dx

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log iintegral 1/( lnlnln(x) lnln(x) ln(x) x) dx

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2nd way: derivative (x^x)√ x

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1st way: If x^y+ y^x=2 then find dy/dx

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