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Differentiate the following w.r.t x sin...

Differentiate the following w.r.t x
`sin^(-1)(2x//1+x^(2))`

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To differentiate the function \( y = \sin^{-1}\left(\frac{2x}{1+x^2}\right) \) with respect to \( x \), we will follow these steps: ### Step 1: Identify the function and its derivative We know that the derivative of \( \sin^{-1}(u) \) with respect to \( x \) is given by: \[ \frac{d}{dx} \sin^{-1}(u) = \frac{1}{\sqrt{1 - u^2}} \cdot \frac{du}{dx} \] where \( u = \frac{2x}{1+x^2} \). ...
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ICSE-VECTORS SCALARS ELEMENTARY CALCULUS -UNSOLVED PROBLEMS
  1. Differentiate w.r.t x (1-cos x)//(1+ cos x)

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  2. Differentiate w.r.t x e^(x) log (sin 2x)

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  3. Differentiate the following w.r.t x sin^(-1)(2x//1+x^(2))

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  4. Differentiate the following w.r.t x cos^(-1) (sqrt(1+x//2))

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  5. Differentiate the following w.r.t x tan^(-1) ((cos x - sin x)/(cos x...

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  6. Find (dy)/(dx) " if " sin x + cos y = xy "

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  7. Differentiate w.r.t x (sinx)^(x) +sin(x^(x))

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  8. Differentiate w.r.t x sqrt(x) (2x+3)^(2)//sqrt(x+1)

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  9. If x = a ( t+ sin t) and y = a (1- cos t) " find " (dy)/(dx)

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  10. Find (dy)/(dx) when x = a cos theta and y = b sin theta

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  11. Find (dy)/(dx) when x = a sec theta and y = b tan theta

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  12. Find the velocity of a particle moving on a line at t = 3 seconds , if...

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  13. Find the velocity of a particle moving on a line at t = 3 seconds , if...

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  14. At time t , the displacement of a particle moving in a straight line ...

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  15. A car is running on a straight road . The distance travelled and time...

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  16. The side of a square sheet of a metal is increasing at 3 cm per minut...

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  17. A stone is dropped into a quiet pond and waves move in circle at a s...

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  18. A particle starts rotating from rest according to the formula theta ...

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  19. The area of dot of ink in cm^(2) is growing such that after 5s , A = ...

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  20. A particle starts rotating from rest according to the formula theta = ...

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