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

Differentiate the following w.r.t. x.
`(sin x)^(tan x) + (cos x)^(sec x)`

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The correct Answer is:
`(sin x)^(tan x) [1 + sec^2 x log sin x] + (cos x)^(sec x)[-sec x tan x + sec x tan x log cos x]`
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
  1. Differentiate the function w.r.t. x : sqrt ((x-1)(x-2))/((x-3)(x-4)(...

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  2. Differentiate the following w.r.t. x. (sin x)^(cos x) + (cos x)^(sin...

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  3. Differentiate the following w.r.t. x. (sin x)^(tan x) + (cos x)^(sec...

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

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  5. Diferentiate tan^(-1)((x)/(sqrt(1 - x^2))) w.r.t.x.

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  6. If y = cos(2 cos^(-1)x), then prove that (1 - x^2)(d^2y)/(dx) -xdy/dx ...

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  7. If y = sin(2 cos^(-1)x), then prove that (1 - x^2)(d^2y)/(dx) -x dy/d...

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  8. Verify Rolle's theorem for the function : f(x) = (x+1)(x-4) in the int...

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  9. Verify Rolle's theorem for the following functions f(x)=(x + 2)(x-3)...

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  10. Verify Rolle's theorem for the following functions f(x) = (x+3)(x-6)...

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  11. Find the values of k so that the function f is continuous at the indic...

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  12. Find the values of k so that the function f is continuous at the indic...

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

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  14. Differentiate the following w.r.t. x : (x + 1/x)^x + x^(x + 1/x)

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  15. Differentiate the following w.r.t. x : x^(x^2 - 3) + (x - 3)^(x^2) ,...

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  16. For what value of k, function f (x) is continuous at x = 0 where f(x) ...

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  17. Find (dy)/(dx) when x^y + y^x = a^b

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  18. Differentiate tan^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + ...

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  19. y = e^(m sin^(-1)x), prove that (1 - x^2) y2 - xy1 = m^2y

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  20. If y = e^(m tan^-1 x), then show that (1 +x^2) y2 + (2x - m) y1= 0.

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