Bonjour
Carolinaaaaa
[tex]a)\ n(x)=(-5x+3)\sqrt{x}\\\\n'(x)=(-5x+3)'\sqrt{x}+(-5x+3)(\sqrt{x})'\\\\n'(x)=-5\sqrt{x}+(-5x+3)\times\dfrac{1}{2\sqrt{x}}\\\\n'(x)=-5\sqrt{x}+\dfrac{-5x+3}{2\sqrt{x}}\\\\n'(x)=\dfrac{-5\sqrt{x}\times2\sqrt{x}-5x+3}{2\sqrt{x}}\\\\n'(x)=\dfrac{-10x-5x+3}{2\sqrt{x}}\\\\n'(x)=\dfrac{-15x+3}{2\sqrt{x}}\\\\\\\boxed{n'(x)=\dfrac{-3(5x-1)}{2\sqrt{x}}}[/tex]
[tex]b)\ p(x)=(2x^2-x+1)(-7x+8)\\\\p'(x)=(2x^2-x+1)'(-7x+8)+(2x^2-x+1)(-7x+8)'\\\\p'(x)=(4x-1)(-7x+8)+(2x^2-x+1)\times(-7)\\\\p'(x)=-28x^2+32x+7x-8-14x^2+7x-7\\\\\boxed{p'(x)=-42x^2+46x-15}[/tex]
[tex]c)\ r(x)=\dfrac{3x-7}{x}\\\\r'(x)=\dfrac{(3x-7)'\times x-(3x-7)\times x'}{x^2}\\\\r'(x)=\dfrac{3\times x-(3x-7)\times1}{x^2}\\\\r'(x)=\dfrac{3x-3x+7}{x^2}\\\\\boxed{r'(x)=\dfrac{7}{x^2}}[/tex]
[tex]d)\ s(x)=\dfrac{x+5}{2x-1}\\\\\\s'(x)=\dfrac{(x+5)'(2x-1)-(x+5)(2x-1)'}{(2x-1)^2}\\\\\\s'(x)=\dfrac{1\times(2x-1)-(x+5)\times2}{(2x-1)^2}\\\\\\s'(x)=\dfrac{2x-1-2x-10}{(2x-1)^2}\\\\\\\boxed{s'(x)=\dfrac{-11}{(2x-1)^2}}[/tex]
[tex]e)\ t(x)=\dfrac{x^2+3x-7}{x+5}\\\\t'(x)=\dfrac{(x^2+3x-7)'(x+5)-(x^2+3x-7)(x+5)'}{(x+5)^2}\\\\t'(x)=\dfrac{(2x+3)(x+5)-(x^2+3x-7)\times1}{(x+5)^2}\\\\t'(x)=\dfrac{2x^2+10x+3x+15-x^2-3x+7}{(x+5)^2}\\\\\boxed{t'(x)=\dfrac{x^2+10x+22}{(x+5)^2}}[/tex]
[tex]f)\ w(x)=\dfrac{5\sqrt{x}}{7-3x}\\\\\\w'(x)=\dfrac{(5\sqrt{x})'(7-3x)-5\sqrt{x}(7-3x)'}{(7-3x)^2}\\\\\\w'(x)=\dfrac{\dfrac{5}{2\sqrt{x}}(7-3x)-5\sqrt{x}\times(-3)}{(7-3x)^2}\\\\\\w'(x)=\dfrac{\dfrac{5}{2\sqrt{x}}(7-3x)+15\sqrt{x}}{(7-3x)^2}\\\\\\w'(x)=\dfrac{5(7-3x)+15\sqrt{x}\times2\sqrt{x}}{2\sqrt{x}(7-3x)^2}\\\\\\w'(x)=\dfrac{35-15x+30x}{2\sqrt{x}(7-3x)^2}\\\\\\w'(x)=\dfrac{35+15x}{2\sqrt{x}(7-3x)^2}\\\\\\\boxed{w'(x)=\dfrac{5(7+3x)}{2(7-3x)^2\sqrt{x}}}[/tex]
