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Find (dy)/(dx) , when x=a\ cos^3t and y=...

Find `(dy)/(dx)` , when `x=a\ cos^3t` and `y=a\ sin^3t` .

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To find \(\frac{dy}{dx}\) when \(x = a \cos^3 t\) and \(y = a \sin^3 t\), we will use the chain rule and implicit differentiation. Here’s a step-by-step solution: ### Step 1: Differentiate \(x\) with respect to \(t\) Given: \[ x = a \cos^3 t \] We differentiate \(x\) with respect to \(t\): ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Find (dy)/(dx): x=a(theta-sintheta) and y=a(1-costheta)

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  2. If x=a\ s e c^3theta and y=a\ t a n^3theta , find (dy)/(dx) at theta=p...

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  3. Find (dy)/(dx) , when x=a\ cos^3t and y=a\ sin^3t .

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  4. If x=sqrt(a^sin^((-1)t)), y=sqrt(a^cos^((-1)t)) , show that (dy)/(dx)=...

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  5. If x=sin^(-1)((2t)/(1+t^2))a n dy=tan^(-1)((2t)/(1-t^2)),t > 1. P rov ...

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  6. If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...

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  7. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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

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

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

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

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

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

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

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

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

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

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

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

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

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