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

Add math: Find the equation of the line ...

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

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) 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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Review: Linear form, Quadratic form & Bilinear form

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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lim x/e^x? as x→∞

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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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Simplify the Boolean function F=A+A'B

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example: Mean, Median & Mode

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1st/2ways: Taylor series of sin(x)

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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integral ∫x^(-1) log(x) dx

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2nd way: integral ∫p^(nx) q^x dx

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2nd way: trig Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫tan^(3/2)(x) sec^4(x) dx

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UC Davis: differentiate y=(3x+1)^2

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