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If x=a((1+t^2)/(1-t^2)) and y=(2t)/(1-t^...

If `x=a((1+t^2)/(1-t^2))` and `y=(2t)/(1-t^2)` , find `(dy)/(dx)`

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To find \(\frac{dy}{dx}\) given the equations: \[ x = a \left( \frac{1 + t^2}{1 - t^2} \right) \] \[ y = \frac{2t}{1 - t^2} \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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  2. If a gt0, x=(t+(1)/(t))^(a) and y=a^((t+(1)/(t))), find (dy)/(dx).

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  3. If x=a((1+t^2)/(1-t^2)) and y=(2t)/(1-t^2) , find (dy)/(dx)

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  6. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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  8. If x=(1+logt)/(t^2),\ \ y=(3+2logt)/t ,\ \ find (dy)/(dx) .

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  9. If x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot

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  10. If sinx=(2t)/(1+t^2) , tany=(2t)/(1-t^2) , find (dy)/(dx) .

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  11. Differentiate logsinx with respect to sqrt(cosx) .

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  12. Differentiate tan^(-1)((1+2x)/(1-2x)) with respect to sqrt(1+4x^2) .

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  13. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ,x...

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  14. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to tan^(-1)x ,-1ltxl...

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  15. Differentiate x^x with respect to xlogx .

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  16. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

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  17. Differentiate x^(sin^(-1)x) with respect to sin^(-1)x .

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  18. If x in (1/(sqrt(2)),\ 1) , differentiate tan^(-1)((sqrt(1-x^2))/x) wi...

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  19. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

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  20. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

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