If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>-</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></mrow></mfrac></mfenced><mo>=</mo><mi>log</mi><mo>&nbsp;</mo><mi mathvariant="normal">a</mi></math>&nbsp;then&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>dy</mi><mi>dx</mi></mfrac><mo>=</mo></math>

The value of the derivative of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>|</mo><mo>+</mo><mo>|</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>|</mo></math>&nbsp;at x=2 is:

If&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mi mathvariant="normal">k</mi></msup><mo>+</mo><msup><mi mathvariant="normal">y</mi><mi mathvariant="normal">k</mi></msup><mo>=</mo><msup><mi mathvariant="normal">a</mi><mi mathvariant="normal">k</mi></msup><mo>(</mo><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">k</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math>&nbsp;and &nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>dy</mi><mi>dx</mi></mfrac><mo>+</mo><msup><mfenced separators="|"><mfrac><mi mathvariant="normal">y</mi><mi mathvariant="normal">x</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>0</mn></math>&nbsp;then k=

The sugar unit present in the nucleotides of RNA is

<math xmlns="http://www.w3.org/1998/Math/MathML"><munder accentunder="false"><mo>lim</mo><mrow><mi>x</mi><mo stretchy="false">→</mo><mn>0</mn></mrow></munder><mo> </mo><mfenced separators="|" close="]" open="["><mrow><mo>min</mo><mfenced separators="|"><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>11</mn></mrow></mfenced><mo>⋅</mo><mfrac><mrow><mi>sin</mi><mo>⁡</mo><mi>x</mi></mrow><mi>x</mi></mfrac></mrow></mfenced></math>&nbsp; &nbsp;(where&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mo>·</mo><mo>]</mo></math>&nbsp;denotes the greatest integer function) is&nbsp;

If ${Sin}^{- 1} (\frac{x^{2} - y^{2}}{x^{2} + y^{2}}) = \log a$ then $\frac{dy}{dx} =$

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If Sin-1x2-y2x2+y2=log a then dydx=

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If ${Sin}^{- 1} (\frac{x^{2} - y^{2}}{x^{2} + y^{2}}) = \log a$ then $\frac{dy}{dx} =$