derivative Find dy/dx where x^y + y^x=1

1st/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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matrix product: AB=0 where A≠0 & B≠0

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UC Davis: differentiate y=2^cot(x)

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#3 2024 MIT Integration Bee Qualifying Exam

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2nd/2 ways: trig integral sin(x)/x + cos(x)/x^2 dx

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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3rd/3ways: trig integral ∫sec(x) dx

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#3 2010 MIT Integration Bee Qualifying Exam

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The Maclaurin series of an EVEN function includes only EVEN powers.

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2nd way: trig sq rt Calculate integral ∫cos √x dx

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trig log integral ∫sin(ln(x^n)) dx

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Wanna know function that is NEITHER even NOR odd? Here you go ...

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#1 2021 MIT Bee Qualifier: trig integral sin(x) cos(x) tan(x) sec(x) csc(x) cot(x) dx

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Screen Recording 2024-02-22 at 10.45.08 PM

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#4 2024 MIT Integration Bee Qualifying Exam

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