AP03-04

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\[\begin{aligned} f_1'(x) &= 2x\mathrm e^x + x^2\mathrm e^x = (2x + x^2)\mathrm e^x\;;&\\ f_2'(x) &= \frac{1\times (x^2 + 1) - (x-3)\times (2x)}{(x^2+1)^2}& \\ &=\frac{x^2 + 1 - 2x^2 + 6x}{(x^2+1)^2} =\frac{-x^2 + 6x + 1}{(x^2 + 1)^2}\;;&\\ f_3'(x) &= (2\times 2x + 5)\mathrm e^{2x^2+5x}=(4x+5)\mathrm e^{2x^2+5x}\;;&\\ f_4'(x) &=6 \times 2(2x - 11)^5 = 12(2x-11)^5.& \end{aligned}\]

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code : 173