derivative x^n vs n^x vs x^x

𝐅𝐢𝐫𝐞𝐰𝐨𝐫𝐤𝐬 - 𝐄𝐩𝐢𝐬𝐨𝐝𝐞 - 17 [𝐄𝐧𝐠 𝐒𝐮𝐛]

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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logic Idempotent law show x=xVx

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STPM Math T Sem2: Find the Maclaurin series for xe^(-x) [ahp kia]

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

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Swinburne U 2nd way: e^(-e^x) e^x dx

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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Find the area via Pick's Theorem

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LILY

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2nd example: Find the sum -0.31, -0.19, -0.07, 0.05, 0.17, 0.29 via median

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trig integral ∫1/(√sin(x) √cos^7(x)) dx

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2nd way: trig integral ∫1/(cos^2(x) - sin^2(x)) dx

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2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)

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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find

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Example: Find the sum

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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3

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trig Show cos(4x) = 8 cos^4(x) -cos^2(x)+1

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Screen Recording 2024-05-12 at 10.30.40 PM

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