https://peda.net/id/8cf556a6499 2020-02-07T12:42:34+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/5346e2804ca 2020-02-11T09:55:48+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1%7D%7B2%7Dx" alt="\frac{1}{2}x"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E1" alt="x&gt;1"/><br/> c)<br/> derivaatta ei ole negatiivinen millään x arvolla, jolla funktio on määritelty 2020-02-11T09:44:25+02:00 https://peda.net/id/b5063e8a4c9 2020-02-11T09:23:00+02:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(3%5Cln%20x%5Cright)%3D3%5Ccdot%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B3%7D%7Bx%7D" alt="D\left(3\ln x\right)=3\cdot\frac{1}{x}=\frac{3}{x}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(%5Cfrac%7B%5Cln%20x%7D%7B3%7D%5Cright)%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20D%5Cleft(%5Cln%20x%5Cright)%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cfrac%7B1%7D%7Bx%7D%3D%5Cfrac%7B1%7D%7B3x%7D" alt="D\left(\frac{\ln x}{3}\right)=\frac{1}{3}\cdot D\left(\ln x\right)=\frac{1}{3}\cdot\frac{1}{x}=\frac{1}{3x}"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%2B%5Cln3x%3D%5Cfrac%7B1%7D%7B3x%7D%5Ccdot3%3D%5Cfrac%7B1%7D%7Bx%7D" alt="3+\ln3x=\frac{1}{3x}\cdot3=\frac{1}{x}"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cln3%2B%5Cln%20x%5E3%3D%5Cfrac%7B1%7D%7Bx%5E3%7D%5Ccdot3x%5E2%3Dx%5E%7B-3%7D%5Ccdot3x%5E2%3D3x%5E%7B-1%7D%3D%5Cfrac%7B3%7D%7Bx%7D" alt="\ln3+\ln x^3=\frac{1}{x^3}\cdot3x^2=x^{-3}\cdot3x^2=3x^{-1}=\frac{3}{x}"/> 2020-02-11T09:11:21+02:00