$\text{Bài 1: }\\\text{a) }y=26x^{100}+26x^{50}-26x^2+26x-26\\\to y'=(26x^{100}+26x^{50}-26x^2+26x-26)'\\\hspace{1cm}=2600x^{99}+1300x^{49}-52x+26\\\text{b) }y=26x^{100}+26x^{50}-26x^2-26\sqrt{x}+26x-26\\\to y'=(26x^{100}+26x^{50}-26x^2-26\sqrt{x}+26x-26)'\\\hspace{1cm}=2600x^{99}+1300x^{49}-52x-26.\dfrac{1}{2\sqrt{x}}+26\\\hspace{1cm}=2600x^{99}+1300x^{49}-52x-\dfrac{13}{\sqrt{x}}+26\\\text{c) }f(x)=(x^{10}-26\sqrt{x}+26)(x^2-26x+26)\\\to f'(x)=(x^{10}-26\sqrt{x}+26)(x^2-26x+26)'\\\hspace{1,7cm}=(x^{10}-26\sqrt{x}+26)'(x^2-26x+26)+(x^{10}-26\sqrt{x}+26)(x^2-26x+26)'\\\hspace{1,7cm}=(10x^9-\dfrac{13}{\sqrt{x}})(x^2-26x+26)+(x^{10}-26\sqrt{x}+26)(2x-26)\\\text{d) }y=\dfrac{26x-10}{26x+20}\\\to y'=\Bigg(\dfrac{26x-10}{26x+20}\Bigg)'\\\hspace{1cm}=\dfrac{(26x-10)'(26x+20)-(26x-10)(26x+20)'}{(26x+20)^2}\\\hspace{1cm}=\dfrac{26(26x+20)-26(26x-10}{(26x+20)^2}\\\hspace{1cm}=\dfrac{780}{(26x+20)^2}\\\text{e) }y=\dfrac{10x+26}{20x-26}\\\to y'=\Bigg(\dfrac{10x+26}{20x-26}\Bigg)'\\\hspace{1cm}=\dfrac{(10x+26)'(20x-26)-(10x+26)(20x-26)'}{(20x-26)^2}\\\hspace{1cm}=\dfrac{10(20x-26)-20(10x+26)}{(20x-26)^2}\\\hspace{1cm}=\dfrac{-780}{(20x-26)^2}\\\text{f) }y=(26x^{20}-26x^7+26x-26)^{10}\\\to y'=\Bigg[(26x^{20}-26x^7+26x-26)^{10}\Bigg]'\\\hspace{1cm}=10(26x^{20}-26x^7+26x-26)^9(26x^20-26x^7+26x-26)'\\\hspace{1cm}=10(26x^{20}-26x^7+26x-26)^9(520x^{19}-182x^6+26)\\\text{g) }y=\sin\sqrt{26x^2-26x+26}\\\to y'=(\sin\sqrt{26x^2-26x+26})'\\\hspace{1cm}=\cos\sqrt{26x^2-26x+26}.(\sqrt{26x^2-26x+26})'\\\hspace{1cm}=\dfrac{1}{2\sqrt{26x^2-26x+26}}.(26x^2-26x+26)'.\cos\sqrt{26x^2-26x+26}\\\hspace{1cm}=\dfrac{52x-26}{2\sqrt{26x^2-26x+26}}.\cos\sqrt{26x^2-26x+26}\\\hspace{1cm}=\dfrac{26x-13}{\sqrt{26x^2-26x+26}}.\cos\sqrt{26x^2-26x+26}\\\text{Bài 2: }\\y=26x^3-26x^2-x+26\\\to y'=78x^2-52x-1\\\to y'_{(x_o)}=25\\\to \text{Phương trình tiếp tuyến: }y=25(x-1)+(26-1)\\\hspace{6,2cm}=25x$
