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

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

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To differentiate the function \( y = (\sin x)^x + \sin(x^x) \) with respect to \( x \), we will break it down into two parts and differentiate each part separately. ### Step 1: Differentiate the first part \( A = (\sin x)^x \) 1. **Rewrite using logarithms**: \[ A = (\sin x)^x \implies \log A = x \log(\sin x) \] ...
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ICSE-VECTORS SCALARS ELEMENTARY CALCULUS -UNSOLVED PROBLEMS
  1. Differentiate the following w.r.t x tan^(-1) ((cos x - sin x)/(cos x...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Integrate the following w.r.t x sqrt(x)

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  18. Integrate the following w.r.t x 2//x^(3//2)

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  19. Integrate the following w.r.t x e^(mx)

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  20. Integrate the following w.r.t x 2^(x)

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