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If y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5...

If `y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5)))`, find `(dy)/(dx)`.

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To find \(\frac{dy}{dx}\) for the function \[ y = \sqrt{\frac{(x-3)(x^2 + 4)}{3x^2 + 4x + 5}}, \] we will use logarithmic differentiation. Here’s the step-by-step solution: ...
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RS AGGARWAL-DIFFERENTIATION-Exercise 10I
  1. If y=sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))), find (dy)/(dx).

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  2. If x=at^2 and y=2at then find the value of ((dy)/(dx))^2

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  3. Find (dy)/(dx), when x=acos theta, y=bsin theta

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

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  5. Find (dy)/(dx), when x=acos^(3)theta,y=a sin^(3)theta

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

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  7. Find (dy)/(dx), when x=alogt,y=bsint

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  8. Find (dy)/(dx), when x=(logt+cost),y=(e^(t)+sint)

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  9. Find (dy)/(dx), when x=costheta+cos2 theta,y=sin theta+sin2theta

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  10. Find (dy)/(dx), when x=sqrt(sin 2theta), y=sqrt(cos 2theta)

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

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

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

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

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

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  16. "If "x=3cost-2cos^(3)t,y=3sint-2sin^(3)t," show that"(dy)/(dx)=cott.

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  17. if x=(1+lnt)/t^2 and y=(3+2lnt)/t then show that y(dy)/(dx)=2x((dy)/(d...

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

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

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  20. If x=sin^3t/(sqrtcos2t), y=cos^3t/sqrt(cos2t) show that dy/dx =0 at t=...

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  21. "If "x=(2costheta-cos 2theta)and y=(2sin theta-sin 2theta)," find "((d...

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