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

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find (dy)/(dx), y=(sinx)^(cosx)+(cosx)^(sinx)

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  15. If y=(x-1)log(x-1)-(x+1)log(x+1), prove : (dy)/(dx)=log((x-1)/(1+x))

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

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  17. If y=(xsin^(-1)x)/(sqrt(1-x^2)),"p r o v et h a t"(1-x^2)(dy)/(dx)=x+...

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  18. Differentiate the following function tan^2x

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  19. If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)

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  20. If x y^2=1,p rov et h a t2(dy)/(dx)+y^3=0

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