# 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
$y=(\sqrt[4]{x}-\frac{1}{2})^{2}$
$y=(x^{\frac{1}{4}}-\frac{1}{2})^{2}$
$y'=2(\sqrt[4]{x}-\frac{1}{2})\cdot\frac{1}{4}{x}^{-\frac{3}{4}}=2(\sqrt[4]{x}-\frac{1}{2})\cdot\frac{1}{16\sqrt{x^{3}}}=\frac{2\sqrt[4]{x}-1}{16\sqrt{x^{3}}}$
## 6

## 7
$y=\cfrac{x^{5}+x^{3}+x}{\sqrt{x}}$
$y'=\cfrac{1}{x}\left((x^{5}+x^{3}+x)\cdot\frac{1}{2\sqrt{x}}-(5x^{4}+3x^2+1)\cdot\sqrt{x}\right)$
## 8
$y=\sqrt[3]{\sqrt{x}x}$
$y'=\frac-{1}{3}$
## 9
## 10
$y=x\cos x$
$y'=\cos x \cdot x-\sin x$
## 11
$y=x^{2}\sin x + \tan x$
$y'=2x(\sin x)\cdot x^2\cos x+\frac{1}{\cos^{2}x}$
## 12
$y=\cfrac{\sin x}{x^3}$
$y'=\frac{1}{x^{6}}\cdot \left(\sin x\cdot 3x^{2}-\cos x\cdot x^{3}\right)$
$y'=\cfrac{\left(\sin x\cdot 3x^{2}-\cos x\cdot x^{3}\right)}{x^6}$
$y'=\frac{3\sin x}{x^4}-\frac{\cos x}{x^{3}}$
## 13
$y=\sqrt{x}\ln x$
$y'=-\cfrac{1}{2\sqrt{x}}\cdot \ln x + \cfrac{1}{x}\cdot\sqrt{x}$
$y'=\cfrac{\sqrt{x}}{x}-\cfrac{\ln x}{2\sqrt{x}}$