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

301 302

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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logic Idempotent law show x=xVx

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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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#5 MIT 2022 Integration Bee Qualifying Exam

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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=

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2nd way: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫sin(x)cos(x)cos(4x)cos(8x)cos(16x)cos(32x)cos(64x) dx

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2 ways: diff eq Solve dy/dx-x^2=0

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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2nd way: Express as partial fractions

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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CMU: Find these integrals (a)-(b)

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1st/2 ways[Direct]: Prove that the sum of 2 ODD numbers is ALWAYS EVEN

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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2 ways: ∫ 1/(10x^2 -x-21) dx

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derivative (f(x)/g(x))^h(x)

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2nd/2parts: Review: Equation of a straight line passing through the point (x1,,y1)...

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Ex11.6 STPM Math T Sem.2 Find the fir st 4 terms in the expansion of the following functions

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