Find dy/dx Q x + y = a

x+y=adifferentiate both sidesd dxx+y=d dxad dxx12+y12=0d dxx12+d dxy12=0Use d dxxn=n xn-112x12-1+12y12-1 dydx=0=x-12+y-12 dydx=0dydx=-x-12y-12=-y12x12=-yx

Find dy/dx

Q. $\sqrt{x} + \sqrt{y} = \sqrt{a}$

\sqrt{x} + \sqrt{y} = \sqrt{a} d i f f e r e n t i a t e b o t h s i d e s \frac{d}{d x} (\sqrt{x} + \sqrt{y}) = \frac{d}{d x} \sqrt{a} \frac{d}{d x} (x^{\frac{1}{2}} + y^{\frac{1}{2}}) = 0 (\frac{d}{d x} x^{\frac{1}{2}} + \frac{d}{d x} y^{\frac{1}{2}}) = 0 U s e \frac{d}{d x} x^{n} = n x^{n - 1} (\frac{1}{2} x^{\frac{1}{2} - 1} + \frac{1}{2} y^{\frac{1}{2} - 1} \frac{d y}{d x}) = 0 = (x^{- \frac{1}{2}} + y^{- \frac{1}{2}} \frac{d y}{d x}) = 0 \frac{d y}{d x} = - \frac{x^{- \frac{1}{2}}}{y^{- \frac{1}{2}}} = - \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}} = - \frac{\sqrt{y}}{\sqrt{x}}

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Find dy/dx Q. x + y = a

Find dy/dx

Q. $\sqrt{x} + \sqrt{y} = \sqrt{a}$