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Transform the differential equation (1-x...

Transform the differential equation `(1-x^2)((d^2y)/(dx^2))=x(dy/dx)` by substituting` x=cos t.`

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A DAS GUPTA-Differentiation-Exercise
  1. If phi(x)= |[1,2x,3x^2], [x,x^2,x^4], [0,2,6x]| then phi'(1)=

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  2. The value of (dy/dx){(1,1)} for the curve 2y = 3 -x^2 is

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  3. Let y =log(e)sin(x^2),0ltxlepi/2. The value of dy/dx at x= sqrt(pi/2) ...

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  4. If f(x) = log ex then the differential coefficent of f(logex) with res...

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  5. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  6. If f(x) = tan^-1 {1/x (sqrt(1+x^2))} then f'(0) is

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  7. If t=e^x and y=t^2-1 then (dy/dx) at t=1 is

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  8. x^3-2x^2y^2+5x+y-5=0, then find (d^2y)/(dx^2) at x=1, y=1

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  9. Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d...

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  10. The derivative of an even function is always an odd function.

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  11. If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may...

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  12. If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

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  13. Q.14 Let f(x) = (ax + b) cosx + (cx + d) sinx andf'(x) = x cosx for al...

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  14. If f(x) = |x - 1| and g(x) = f(f(f(x))) then for x gt 2, g'(x) =

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  15. (d(x^(logx)))/(d(logx))=

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  16. Find dy/dx in terms of x if t= x/(1+x^2), y=x^2+t^2.

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  17. If g is the inverse of a function f and f'(x) = 1/(1+x^(5)), then g'(x...

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  18. If y=f(x),p=(dy)/(dx) and q=(d^(2)y)/(dx^(2)), then what is (d^(2)x)/(...

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  19. Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists. Prove that f'(...

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  20. Transform the differential equation (1-x^2)((d^2y)/(dx^2))=x(dy/dx) by...

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