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If y=x^(y), show that dy/dx=y^(2)/(x(1-y...

If `y=x^(y)`, show that `dy/dx=y^(2)/(x(1-ylogx))`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(i) (LONG ANSWER TYPE QUESTIONS (I))
  1. Differentiate the following w.r.t. x : x^(2)e^(x)sinx

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  2. Differentiate the following w.r.t. x : e^(x)cos^(3)xsin^(2)x

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  3. Differentiate the following w.r.t. x : (x+3)^(2)(x+4)^(3)(x+5)^(4)

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  4. Differentiate the following w.r.t. x : sqrt((x-1)(x-2)(x-3)(x-4))

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  5. If x y=e^(x-y) , find (dy)/(dx) .

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  6. If (sinx)^(y)=(siny)^(x),"find "dy/dx.

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  7. Find dy/dx" if "(sinx)^(cosy)=(cosy)^(sinx).

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  8. Differentiate log(x^(x)+cosec^(2)x) w.r.t. x.

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  9. If x^(p)y^(q)=(x+y)^(p+q), show that dy/dx=y/x.

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  10. If y=x^(y), show that dy/dx=y^(2)/(x(1-ylogx))

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  11. If y^(x)=e^(y-x), then prove that (dy)/(dx) = ((1+logy)^(2))/(logy)

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  12. If x^x+y^x=1 , prove that (dy)/(dx)=-{(x^x(1+logx)+y^x logy)/(x y^((x...

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  13. If x^(y)+y^(x)=1,"find "dy/dx

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  14. If x^y+y^x=a^b , then find dy/dx.

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  15. If x^(y)+y^(x)=4,"find "dy/dx

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  16. If x^(y)+y^(x)=loga,"find "dy/dx.

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  17. Show that if x^(y)+y^(x)=m^(n), then : dy/dx=-(y^(x)logy+yx^(y-1))/(...

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  18. Find the derivative of the function given by : f(x)=(1+x)(1+x^(2))(1...

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  19. Differentiate (x^2-5x+8)(x^3+7x+9) in three ways mentioned below:(i) ...

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  20. If u, v and w are functions of x, then show thatd/(dx)(udotvdotw)=(d u...

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