सोल्यूशन - व्युत्पन्न

उत्पादन नियमाचा वापर करणे.

$$\frac{d}{dx}[4\times \frac{{\left(xy\right)}^1}{2}]=\frac{d}{dx}\left[4\right]\times \frac{{\left(xy\right)}^1}{2}+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]$$

स्थिर मूल्याचे अभिषेक सदैव शून्य असते.

$$\frac{d}{dx}\left[4\right]\times \frac{{\left(xy\right)}^1}{2}+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]=0\times \frac{{\left(xy\right)}^1}{2}+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]$$

कोणतीही संख्या शून्याने गुणक करतल्यास निवडकत:Is always equal to zero.

$$0\times \frac{{\left(xy\right)}^1}{2}+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]=0+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]$$

एकाच्या संख्येला शून्य जोडणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

$$0+4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]=4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]$$

भिन्नाच्या व्युत्पन्न गणना करा.

$$4\times \frac{d}{dx}\left[\frac{{\left(xy\right)}^1}{2}\right]=4\times \frac{\frac{d}{dx}\left[{\left(xy\right)}^1\right]\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}$$

सत्तेच्या फंक्शनच्या व्युत्पन्न गणना करा.

$$4\times \frac{\frac{d}{dx}\left[{\left(xy\right)}^1\right]\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}=4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}$$

स्थिर मूल्याचे अभिषेक सदैव शून्य असते.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times \frac{d}{dx}\left[2\right]}{2^2}=4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{2^2}$$

अंकगणित प्रक्रियांचे सरलीकरण करा.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{2^2}=4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}$$

स्थिर मूल्याचे अभिषेक सदैव शून्य असते.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(\frac{d}{dx}\left[1\right]\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}=4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}$$

उत्पादन नियमाचा वापर करणे.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \frac{d}{dx}\left[xy\right]\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}=4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}$$

कोणतीही संख्या शून्याने गुणक करतल्यास निवडकत:Is always equal to zero.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2-{\left(xy\right)}^1\times 0}{4}=4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2+0}{4}$$

एकाच्या संख्येला शून्य जोडणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2+0}{4}=4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$

अंकगणित प्रक्रियांचे सरलीकरण करा.

$$4\times \frac{\left({\left(xy\right)}^1\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$

कोणतीही संख्या शून्याने गुणक करतल्यास निवडकत:Is always equal to zero.

$$4\times \frac{\left(xy\times \left(0\times \ln \left(xy\right)+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(0+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$

स्वत: च्या सपेक्षा व्हेरिएबलचे अभिषेक सदैव एकाशी समान असते.

$$4\times \frac{\left(xy\times \left(0+\frac{1}{xy}\times \left(\frac{d}{dx}\left[x\right]\times y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(0+\frac{1}{xy}\times \left(1y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$

एकाच्या संख्येला शून्य जोडणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

$$4\times \frac{\left(xy\times \left(0+\frac{1}{xy}\times \left(1y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(\frac{1}{xy}\times \left(1y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$

एकाने गुणकरण करणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

$$4\times \frac{\left(xy\times \left(\frac{1}{xy}\times \left(1y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}=4\times \frac{\left(xy\times \left(\frac{1}{xy}\times \left(y+x\times \frac{d}{dx}\left[y\right]\right)\right)\right)\times 2}{4}$$