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Find (dy)/(dx) , when x=acostheta and y=...

Find `(dy)/(dx)` , when `x=acostheta` and `y=bsintheta`

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To find \(\frac{dy}{dx}\) when \(x = a \cos \theta\) and \(y = b \sin \theta\), we will follow these steps: ### Step 1: Differentiate \(x\) with respect to \(\theta\) Given: \[ x = a \cos \theta \] Differentiating \(x\) with respect to \(\theta\): ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Find (dy)/(dx) , when x=a t^2 and y=2\ a t

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  2. Find (dy)/(dx) , when x=a(theta+sintheta) and y=a(1-costheta)

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  3. Find (dy)/(dx) , when x=acostheta and y=bsintheta

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  4. Find (dy)/(dx) , when x=a e^(theta)(sintheta-costheta),\ \ y=a e^(thet...

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  5. Find (dy)/(dx) , when x=b\ sin^2theta and y=a\ cos^2theta

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  6. Find (dy)/(dx) , when x=a(1-costheta) and y=a(theta+sintheta) at theta...

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  7. Find (dy)/(dx) , when x=(e^t+e^(-t))/2 and y=(e^t-e^(-t))/2

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

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  9. Find (dy)/(dx) , when x=a\ (costheta+thetasintheta) and y=a(sintheta-t...

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  10. Find (dy)/(dx) , when x=e^(theta)(theta+1/theta) and y=e^(-theta)(thet...

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

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  12. Find (dy)/(dx) , when x=cos^(-1)1/(sqrt(1+t^2)) and y=sin^(-1)t/(sqrt(...

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  13. Find (dy)/(dx) , when x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2)

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  14. If x=2costheta-cos2\ theta and y=2sintheta-sin2\ theta , prove that (d...

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  15. If x=e^(cos2t) and y=e^(sin2t) , prove that (dy)/(dx)=-(ylogx)/(xlogy)

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  16. If x=cost and y=sint , prove that (dy)/(dx)=1/(sqrt(3)) at t=(2pi)/3

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  17. If x=a(t+1/t) and y=a(t-1/t) , prove that (dy)/(dx)=x/y

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  18. If x=sin^(-1)((2t)/(1+t^2)) and y=tan^(-1)((2t)/(1-t^2)) , -1<t<1 , pr...

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  19. If x and y are connected parametrically by the equations given, wit...

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  20. If a gt0, x=(t+(1)/(t))^(a) and y=a^((t+(1)/(t))), find (dy)/(dx).

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