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If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2...

If `f^(prime)(x)=sqrt(2x^2-1)` and `y=f(x^2)` , then find `(dy)/(dx)` at `x=1` .

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If f^(prime)(1)=2 and y=f((log)e x) , find (dy)/(dx) at x=e .

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  2. If f(1)=4 , f^(prime)(1)=2 , find the value of the derivative of lo...

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  3. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...

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  4. Let g(x) be the inverse of an invertible function f(x) which is deri...

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  5. If y=sin^(-1)(sinx) , -pi/2lt=xlt=pi/2 . Then, write the value of (...

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  6. Find dy/dx if x=sin2y

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  7. If pilt=xlt=2pi and y=cos^(-1)(cosx) , find (dy)/(dx) .

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  8. Find dy/dx if x=sin^2y

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  9. If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , wr...

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  10. If y=x|x| , find (dy)/(dx) for x<0 .

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  11. If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

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  12. If x=a(theta+sintheta),\ \ y=a(1+costheta) , find (dy)/(dx) .

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

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  14. If y=tan^(-1)((1-x)/(1+x)) , find (dy)/(dx) .

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  15. If y=(log)a x , find (dy)/(dx) .

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  16. If y=logsqrt(tanx) , write (dy)/(dx) .

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  17. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

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  18. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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  19. If |x|<1 and y=1+x+x^2+\ ddotto\ oo , then find the value of (dy)/(...

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  20. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1<x<...

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