If y -1-22-x2- find- d y-d x

Put (a^2 x^2)=t, so ,that ,y=1/√(t)=t^ 1/2and t=(a^2 x^2). ∴dy/dx= 1/2t^ 3/2and dt/dx= 2x. So, dy/dx=( dy/dx×dt/dx) =( 1/2t^ 3/2)( 2x)=xt^ 3/2=x(a^2 x^2)^ 3/2 ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

If y =1/√22-x...

Question

If $y = \frac{1}{\sqrt{a^{2} - x^{2}}}, f i n d, \frac{d y}{d x}$ .

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Solution

Put $(a^{2} - x^{2}) = t, s o, t h a t, y = \frac{1}{\sqrt{t}} = t^{- 1 / 2} a n d t = (a^{2} - x^{2}) .$

$∴ \frac{d y}{d x} = - \frac{1}{2} t^{- 3 / 2} a n d \frac{d t}{d x} = - 2 x .$

So, $\frac{d y}{d x} = (\frac{d y}{d x} \times \frac{d t}{d x})$

= $(- \frac{1}{2} t^{- 3 / 2}) (- 2 x) = x t^{- 3 / 2} = x (a^{2} - x^{2})^{- 3 / 2}$

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If y=1√a2−x2,find,dydx.

Put (a2−x2)=t,so,that,y=1√t=t−1/2and t=(a2−x2). ∴dydx=−12t−3/2anddtdx=−2x. So, dydx=(dydx×dtdx) =(−12t−3/2)(−2x)=xt−3/2=x(a2−x2)−3/2

If $y = \frac{1}{\sqrt{a^{2} - x^{2}}}, f i n d, \frac{d y}{d x}$ .