642 B
642 B
Wyznaczyć pochodne podanych funkcji.
1
y=(3-x^{4})^{2}
y'=2(3-x^{4})\cdot(-4x^{3})=(6-2x^{4})\cdot(-4x^{3})=-24x^{3}+8x^{7}
2
y=1-\frac{4}{x^6}+\frac{3}{x^7}
y'=-4\cdot-6x^{-7}+3\cdot-7x^{-8}=\frac{24}{x^{7}}-\frac{21}{x^{8}}
3
y=\cfrac{x^{2}+4}{x}
y'=\cfrac{1}{x^{2}}\cdot\left(2x^{2}-(x^{2}+4)\right)=\cfrac{x^{2}-4}{x^{2}}=1-\cfrac{4}{x^2}
4
y=\cfrac{x-3}{x^{2}}
y'=\cfrac{1}{x^{4}}\cdot\left(x^{2}-2x^{2}+6x\right)=\cfrac{6x-x^{2}}{x^{4}}=\cfrac{6-x}{x^3}
5
y
7
y=\cfrac{x^{5}+x^{3}+x}{\sqrt{x}}
y'=\cfrac{1}{x}\left((x^{5}+x^{3}+x)\cdot\frac{1}{2\sqrt{x}}-(5x^{4}+3x^2+1)\cdot\sqrt{x}\right)