Simplify - dydx- a 2 - x 2 a 2 - x 2

dydx=√(a^2 x^2a^2+x^2)= 2x(a^2+x^2) 2x(a^2 x^2)(a^2+x^2)^22√(a^2 x^2a^2+x^2) = 2x(2a^2)(a^2+x^2)^2×√(a^2+x^2)2√(a^2 x^2) = 2a^2x(a^2+x^2)^3/2(a ...

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Complex Numbers

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Question

Simplify :
$\frac{d y}{d x} = \sqrt{\frac{a^{2} - x^{2}}{a^{2} + x^{2}}}$

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Solution

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\int_{0}^{a} x \sqrt{\frac{a^{2} - x^{2}}{a^{2} + x^{2}}} d x

y = x \sqrt{a^{2} + x^{2}} + a^{2} log (x + \sqrt{a^{2} + x^{2}})

\frac{d y}{d x} = 2 \sqrt{a^{2} + x^{2}}

y = \frac{\sqrt{(a^{2} + x^{2})} + \sqrt{(a^{2} - x^{2})}}{\sqrt{(a^{2} + x^{2})} - \sqrt{(a^{2} - x^{2})}}

\frac{d y}{d x} = - \frac{2 a^{2}}{x^{3}} {1 + \frac{a^{2}}{\sqrt{(a^{4} - x^{4})}}}

\frac{d}{d x} \{\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} \sin^{- 1} \frac{x}{a}\} = \sqrt{a^{2} - x^{2}}

y = \sqrt{x^{2} + a^{2}}, \frac{d y}{d x} =

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