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Find the derivative w.r.t. x: x^(x^(2)...

Find the derivative w.r.t. x:
`x^(x^(2))+a^(x^(2))`

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The correct Answer is:
`x^(x^(2)+1)(1+2log x)+2x*a^(x^(2))*log_(e)a`
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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Long Answer Type Questions)
  1. Find (dy)/(dx) using the rule (dy)/(dx)=(dy)/(du)*(du)/(dv)*(dv)/(dx):...

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  2. If the inverse function of y=f(x) is x=g(y) and f'(x)=(1)/(1+x^(2)), t...

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  3. Find the derivative w.r.t. x: x^(x^(2))+a^(x^(2))

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

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  5. Find the derivative w.r.t. x: (sin x)^(cosx)+e^(3x)

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  6. Find the derivative w.r.t. x: x^(x)+(sinx)^(x)

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  7. Find the derivative w.r.t. x: (tan x)^(cotx)+(cotx)^(tanx)

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

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

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

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

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

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

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

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

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

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

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

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

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

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