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If y=e^x+e^-x, prove that (dy)/(dx)=sq...

If `y=e^x+e^-x`, prove that `(dy)/(dx)=sqrt(y^2-4)`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function with respect to x:x^(1/x)

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  2. If y=sqrt(x^2+a^2)," prove that "y(dy)/(dx)-x=0

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  3. If y=e^x+e^-x, prove that (dy)/(dx)=sqrt(y^2-4)

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  4. If x y=4,prove , x((dy)/(dx)+y^2)=3y

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  5. Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)

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  6. Differentiate the following with respect to x : cos^(-1)(sinx) and cot...

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  7. If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)),0ltxlt1, prove t...

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  8. Differentiate the following function with respect to x : tan^(-1)(...

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  9. If y=cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))}...

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  10. Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

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  11. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

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  12. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  13. Differentiate the following function with respect to x : tan^(-1)(...

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  14. Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

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  15. Differentiate the following function with respect to x : tan^(-1)(...

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  16. Find (dy)/(dx), y=e^x+10^x+x^x

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  17. Differentiate the following function with respect to x : tan^(-1){...

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  18. Differentiate the following function with respect to x : sin^(-1)(...

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  19. Differentiate the following function with respect to x:sin(x^x)

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  20. Differentiate the following function with respect to x : (logx)^(logx)

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