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

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

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To find \(\frac{dy}{dx}\) given \(x = \frac{1 + \log t}{t^2}\) and \(y = \frac{3 + 2 \log t}{t}\), we will use the chain rule and the quotient rule for differentiation. ### Step 1: Differentiate \(x\) with respect to \(t\) Given: \[ x = \frac{1 + \log t}{t^2} \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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  2. If x=cost(3-2\ cos^2t) and y=sint(3-2s in^2t) find the value of (dy)/(...

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

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

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

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

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

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

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

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  10. Differentiate x^x with respect to xlogx .

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

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

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

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

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

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

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  17. If -1/(sqrt(3))ltxlt1/(sqrt(3)) , differentiate tan^(-1)((3x-x^3)/(1-3...

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  18. Differentiate x^2 with respect to x^3 .

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

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  20. Differentiate (logx)^x with respect to logx .

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