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Differentiate the following with respect...

Differentiate the following with respect to `x :` `cos^(-1)(sinx)` and `cot^(-1)((1-x)/(1+x))`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If x y=4,prove , x((dy)/(dx)+y^2)=3y

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Differentiate the following function with respect to x: 10^(logsin...

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  19. If y=logsqrt((1+tanx)/(1-tanx)),"Prove that " (dy)/(dx)=sec2x

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  20. If y=log(sqrt(x)+sqrt(1/x)), prove that (dy)/(dx)=(x-1)/(2x(x+1))

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