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trig derivative differentiate x^sin(x) + (sin(x))^cos(x)
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1st way: exp ∫(e^x)/x (1+x log(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 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 Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers
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trig integral ∫1/cos(ax+b) dx
trig integral ∫1/(cos(x)(1+cos(x)) dx
1st/2ways: Taylor series of cos(x)
5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number
exp integral ∫1/(e^(ax+b) (1+e^(ax+b)) dx
2nd/2ways: trig integral cos(2x)/(cos^2(x) sin^2(x)) dx
3 ways: If y=x/(1+x^2) find dy/dx.
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exp derivative e^f(g(x)) h(x)
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Review count Common mistake Rearrangement LOOT=4!/2 vs LULL NOT = 4!/3
UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
2 ways: ∫x√(x+1) dx
2 ways: log derivative y=ln(a+b)
2nd way: integral ∫1/(a + √√b (x^2)) dx
2nd/2ways: Find lim (z^3-8)/(z-2) for z tends to 2