https://peda.net/id/ceec264c1be 2019-12-11T10:11:18+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/53bb17bc203 2019-12-16T21:57:45+02:00 <div>a) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x%5E2%2B3%5Cright)%5E%7B11%7D" alt="f\left(x\right)=\left(x^2+3\right)^{11}"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3Dx%5E2%2B3" alt="s\left(x\right)=x^2+3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3Dx%5E%7B11%7D" alt="u\left(x\right)=x^{11}"/></div> <div>b) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(x%5E2%2B3%5Cright)%5E%7B11%7D" alt="f\left(x\right)=\left(x^2+3\right)^{11}"/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=11%5Ccdot%5Cleft(x%5E2%2B3%5Cright)%5E%7B10%7D%5Ccdot2x%3D22x%5Cleft(x%5E2%2B3%5Cright)%5E%7B10%7D" alt="11\cdot\left(x^2+3\right)^{10}\cdot2x=22x\left(x^2+3\right)^{10}"/></div> <div> </div> 2019-12-16T21:57:45+02:00 https://peda.net/id/3f4174de203 2019-12-16T21:57:10+02:00 <div class="main"> <div class="content enclose"> <div>a) <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Cleft(4x%2B2%5Cright)%5E4" alt="f\left(x\right)=\left(4x+2\right)^4"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3D4x%2B2" alt="s\left(x\right)=4x+2"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D4" alt="s'\left(x\right)=4"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3Dx%5E4" alt="u\left(x\right)=x^4"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D4x%5E3" alt="u'\left(x\right)=4x^3"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=4%5Ccdot%5Cleft(4x%2B2%5Cright)%5E3%5Ccdot4%3D16%5Ccdot%5Cleft(4x%2B2%5Cright)%5E3" alt="4\cdot\left(4x+2\right)^3\cdot4=16\cdot\left(4x+2\right)^3"/></div> <div>b) <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Csin2x" alt="f\left(x\right)=\sin2x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3D2x" alt="s\left(x\right)=2x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D2" alt="s'\left(x\right)=2"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3D%5Csin%20x" alt="u\left(x\right)=\sin x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D%5Ccos%20x" alt="u'\left(x\right)=\cos x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Ccdot%5Cleft(2x%5Cright)%5Ccdot2%3D2%5Ccos2x" alt="\cos\cdot\left(2x\right)\cdot2=2\cos2x"/></div> <div>c) <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D%5Ccos3x" alt="f\left(x\right)=\cos3x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3D3x" alt="s\left(x\right)=3x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D3" alt="s'\left(x\right)=3"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3D%5Ccos%20x" alt="u\left(x\right)=\cos x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D-%5Csin%20x" alt="u'\left(x\right)=-\sin x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-%5Csin%5Cleft(3x%5Cright)%5Ccdot3%3D-3%5Csin3x" alt="-\sin\left(3x\right)\cdot3=-3\sin3x"/></div> </div> </div> 2019-12-16T21:57:10+02:00 https://peda.net/id/8fcbb2da203 2019-12-16T21:52:16+02:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/></div> <div>a) <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(-2x%2B4%5Cright)%5E6" alt="D\left(-2x+4\right)^6"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3D-2x%2B4" alt="s\left(x\right)=-2x+4"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D-2" alt="s'\left(x\right)=-2"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3Dx%5E6" alt="u\left(x\right)=x^6"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D6x%5E5" alt="u'\left(x\right)=6x^5"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=6%5Cleft(-2x%2B4%5Cright)%5E5%5Ccdot%5Cleft(-2%5Cright)%3D-12%5Cleft(-2x%2B4%5Cright)%5E5" alt="6\left(-2x+4\right)^5\cdot\left(-2\right)=-12\left(-2x+4\right)^5"/></div> <div> </div> <div>b) <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(x%5E2-1%5Cright)%5E5" alt="D\left(x^2-1\right)^5"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3Dx%5E2-1" alt="s\left(x\right)=x^2-1"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D2x" alt="s'\left(x\right)=2x"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3Dx%5E5" alt="u\left(x\right)=x^5"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D5x%5E4" alt="u'\left(x\right)=5x^4"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=5%5Cleft(x%5E2-1%5Cright)%5E4%5Ccdot2x%3D10x%5Cleft(x%5E2-1%5Cright)%5E4" alt="5\left(x^2-1\right)^4\cdot2x=10x\left(x^2-1\right)^4"/></div> <div> </div> <div> </div> <div>c) <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Csin%20x%5E2" alt="D\sin x^2"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Cleft(u%5Cleft(s%5Cleft(x%5Cright)%5Cright)%5Cright)%3Du'%5Cleft(s%5Cleft(x%5Cright)%5Cright)s'%5Cleft(x%5Cright)" alt="D\left(u\left(s\left(x\right)\right)\right)=u'\left(s\left(x\right)\right)s'\left(x\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3Dx%5E2" alt="s\left(x\right)=x^2"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D2x" alt="s'\left(x\right)=2x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3D%5Csin%20x" alt="u\left(x\right)=\sin x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D%5Ccos%20x" alt="u'\left(x\right)=\cos x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Cleft(x%5E2%5Cright)%5Ccdot2x%3D2x%5Ccdot%5Ccos%20x%5E2" alt="\cos\left(x^2\right)\cdot2x=2x\cdot\cos x^2"/></div> <div> </div> <div>d) <img src="https://math-demo.abitti.fi/math.svg?latex=D%5Ccos%5E2x%3DD%5C%20%5Cleft(%5Ccos%20x%5Cright)%5E2" alt="D\cos^2x=D\ \left(\cos x\right)^2"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=s%5Cleft(x%5Cright)%3D%5Ccos%20x" alt="s\left(x\right)=\cos x"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=s'%5Cleft(x%5Cright)%3D-%5Csin%20x" alt="s'\left(x\right)=-\sin x"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=u%5Cleft(x%5Cright)%3Dx%5E2" alt="u\left(x\right)=x^2"/>, <img src="https://math-demo.abitti.fi/math.svg?latex=u'%5Cleft(x%5Cright)%3D2x" alt="u'\left(x\right)=2x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cleft(%5Ccos%20x%5Cright)%5Ccdot%5Cleft(-%5Csin%20x%5Cright)%3D-2%5Csin%20x%5Ccdot%5Cleft(%5Ccos%20x%5Cright)" alt="2\left(\cos x\right)\cdot\left(-\sin x\right)=-2\sin x\cdot\left(\cos x\right)"/></div> 2019-12-16T21:52:16+02:00