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$$y=x\ln(x)\\ y'=1+\ln(x)\\ y''=\frac{1}{x}\\ y'''=-\frac{1}{x^2}$$ $$y^n=(-1)^{n}\frac{(n-2)!}{x^{n-1}}$$ for n>1 clearly $$y=x^3+e^{2x}\\y'=3x^2+2e^{2x} \\ y''=6x+4e^{2x} \\ y'''=6+8e^{2x}\\ y^n=2^n*e^{2x}$$ for n>3 16 is way too much work idk how to approach it without doing a shit ton of quotient rules whcih i dont really want ot do right now lol $$y=\frac{1}{(2x-3)^2}\\y'=\frac{-4}{(2x-3)^3}\\y''=\frac{24}{(2x-3)^4}\\ y'''=\frac{-192}{(2x-4)^5}\\y^n=(-1)^n\frac{2^n(n+1)!}{(2x-3)^{n+2}}$$
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Mon, 15 Oct 2018 05:33 GMT