exp derivative (log f(ax+b) (g(cx+d)))^h(mx+n)

3 ways: If y=x/(1+x^2) find dy/dx.

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

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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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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Bijection of elements in tn & a pair of elements of (n+1)

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2 ways: sq root derivative 1/(√√(1/√x))

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Review: Linear form, Quadratic form & Bilinear form

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

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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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trig integral a) ∫csc^2(x) dx

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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exp integral ∫(e^x +1)^3 dx

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Ax+By+C=0 to x/a + y/b=1

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2nd way: trig derivative tan(arc tan(x))

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2nd way: trig differentiate (log(x))^cos(x)

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Screen Recording 2023-12-30 at 9.34.01 PM

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Screen Recording 2024-02-21 at 10.02.50 PM

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2nd way: integral a^sqrt(x) dx

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Screen Recording 2024-02-22 at 12.00.24 AM

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