सोल्यूशन - व्युत्पन्न

व्युत्पन्नांच्या बेरीज नियमाचा वापर करा.

$$\frac{d}{dx}[x{y}^2+x^{2}y]=\frac{d}{dx}\left[x{y}^2\right]+\frac{d}{dx}\left[x^{2}y\right]$$

उत्पादन नियमाचा वापर करणे.

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

उत्पादन नियमाचा वापर करणे.

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

स्वत: च्या सपेक्षा व्हेरिएबलचे अभिषेक सदैव एकाशी समान असते.

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

सत्तेच्या फंक्शनच्या व्युत्पन्न गणना करा.

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

x raised to the power of n च्या व्युत्पन्न गणना करा.

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

एक अंक वगळा.

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

एकाची सत्ता कोणतीही संख्या असो, ती स्वतःचीच संख्या आहे.

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

एकाने गुणकरण करणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

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

स्थिर मूल्याचे अभिषेक सदैव शून्य असते.

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

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

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

अंकगणित प्रक्रियांचे सरलीकरण करा.

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

एकाच्या संख्येला शून्य जोडणे, ज्यामुळे त्याची मूल्यमान बदलत नाही.

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