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Find the derivative w.r.t. x: e^(cos^...

Find the derivative w.r.t. x:
`e^(cos^(-1)x) +x^(sqrt(x))`

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The correct Answer is:
`-e^(cos^(-1)x)*(1)/(sqrt(1-x^(2)))+x^(sqrt(x))*(2+log x)/(2sqrt(x))`
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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Long Answer Type Questions)
  1. Find the derivative w.r.t. x: (tan x)^(cotx)+(cotx)^(tanx)

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  2. Find the derivative w.r.t. x: (sin x)^(cos x)+(cosx)^(sin x)

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  3. Find the derivative w.r.t. x: e^(cos^(-1)x) +x^(sqrt(x))

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  4. Find the derivative w.r.t. x: (sin x)^(tan x)+(cos x)^(sec x)

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  5. Find the derivative w.r.t. x: x^(sinx)+(sin x)^(cosx)

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  6. Find the derivative w.r.t. x: y^(x)+x^(y)=a^(b)

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  7. Find (dy)/(dx) when : x^(y)+y^(x)=a

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  8. Find (dy)/(dx) when : y=log sqrt((1-cosx)/(1+cosx))+a^(x)

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  9. Find (dy)/(dx) when : y= (x^(3)* sqrt(x^(2)-12))/( 3 sqrt(20-3x))" w...

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  10. Find (dy)/(dx) when : tan^(2)y=(1+cos 2x)/(1-cos2x)

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  11. Find (dy)/(dx) when : e^(y)-(a+b tan x)/(a-b tan x)=0

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  12. Find (dy)/(dx) when : y= 2 tan^(-1) sqrt((x-a)/(b-x))

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  13. Find (dy)/(dx) when : y="cos"^(-1)(a+b cos x)/(b+a cos x)(b gt a)

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  14. Find (dy)/(dx) when : y= tan^(-1)[sqrt((a-b)/(a+b))"tan"(x)/(2)]

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  15. Find (dy)/(dx) when : y=sin[2 tan^(-1) sqrt((1-x)/(1+x))]

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  16. Find (dy)/(dx) when : y="sin"^(-1) (1)/(sqrt(1+x^(2)))+tan^(-1) ( (...

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  17. Find (dy)/(dx) when : x^(sin y)+y^(sinx)=1

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  18. If y=[(tan x)^(tan x)]^(tan x)," find " (dy)/(dx)" at " x=(pi)/(4).

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  19. If y=(1+sin theta+cos theta)/(1+sin theta-cos theta)," show that, " (...

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  20. If tan y=(tan x+sec x-1)/(tan x-sec x+1), " show that, " (dy)/(dx)=(1...

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