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If y = (sin x)^(cos x) find (dy)/(dx)....

If `y = (sin x)^(cos x) ` find `(dy)/(dx)`.

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The correct Answer is:
`(sin x)(cos x. cot x - sin x. log (tan x))`
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. If sin y = x cos (a + y), prove that (dy)/(dx) = (cos^2 (a + y))/(cos ...

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  2. x = a (theta - sin theta), y = a (1 + cos theta) find dy/dx

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  3. If y = (sin x)^(cos x) find (dy)/(dx).

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  4. If y = (cos x)^(sin x) find (dy)/(dx)

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  5. Differentiate cos^(-1)((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)x.

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  6. Differentiate sin^(-1)((2x)/(1 + x^2)) w.r.t. tan^(-1) x.

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  7. Differentiate tan^(-1)(2x)/(1 - x^2) w.r.t. tan^(-1) x.

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

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  9. y = [x + sqrt(x^2 + 1)]^p , prove that (x^2 + 1)y2 + xy1 - p^2y = 0

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  10. Verify Rolle's theorem for the following functions f(x) = (x + 2)(x-...

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  11. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-6) i...

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  12. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-4)^2...

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  13. Verify Rolle's theorem for the following functions f(x)=(x - 1)(x - ...

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  14. Discuss the continuity of the following function: f(x) = sinx - cosx

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  15. Discuss the continuity of the following function: f(x) = sinx cdot cos...

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  16. Discuss the continuity of the following functions f(x) = {{:(x + 2",...

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  17. Determine the value of k so that following functions are continuous at...

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  18. Determine, k if the following function is continuous at x = 0 f(x) =...

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

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  20. Differentiate the following w.r.t. x log (x + sqrt(1 + x^2))

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