z=tan (y+a x)+sqrt{y-a x} Rightarrow z_{x x}- | vedclass

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(A) दिया गया है,$z=	an (y+a x)+\sqrt{y-a x}$ सबसे पहले,$x$ के सापेक्ष आंशिक अवकलन ज्ञात करें: $z_x = \frac{\partial z}{\partial x} = a \sec^2(y+ax) -

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(A) दिया गया है,$z=	an (y+a x)+\sqrt{y-a x}$ सबसे पहले,$x$ के सापेक्ष आंशिक अवकलन ज्ञात करें: $z_x = \frac{\partial z}{\partial x} = a \sec^2(y+ax) - \frac{a}{2\sqrt{y-ax}}$ $z_{xx} = \frac{\partial^2 z}{\partial x^2} = 2a^2 \sec^2(y+ax) 	an(y+ax) - \frac{a^2}{4(y-ax)^{3/2}}$ इसके बाद,$y$ के सापेक्ष आंशिक अवकलन ज्ञात करें: $z_y = \frac{\partial z}{\partial y} = \sec^2(y+ax) + \frac{1}{2\sqrt{y-ax}}$ $z_{yy} = \frac{\partial^2 z}{\partial y^2} = 2 \sec^2(y+ax) 	an(y+ax) - \frac{1}{4(y-ax)^{3/2}}$ अब,$z_{xx} - a^2 z_{yy}$ की गणना करें: $z_{xx} - a^2 z_{yy} = [2a^2 \sec^2(y+ax) 	an(y+ax) - \frac{a^2}{4(y-ax)^{3/2}}] - a^2 [2 \sec^2(y+ax) 	an(y+ax) - \frac{1}{4(y-ax)^{3/2}}]$ $z_{xx} - a^2 z_{yy} = 2a^2 \sec^2(y+ax) 	an(y+ax) - \frac{a^2}{4(y-ax)^{3/2}} - 2a^2 \sec^2(y+ax) 	an(y+ax) + \frac{a^2}{4(y-ax)^{3/2}} = 0$

$z=\tan (y+a x)+\sqrt{y-a x} \Rightarrow z_{x x}-a^2 z_{y y}$ का मान ज्ञात कीजिए।

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