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If x=acos^30theta,y=bsin^30theta, find d...

If `x=acos^30theta,y=bsin^30theta,` find `dy/dx`.

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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. If y=tan^-1((3x-x^3)/(1-x^2)), find dy/dx.

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  2. If x=a((1+t^2)/(1-t^2)),y=(2t)/(1-t^2) find dy/dx at t=1/sqrt3.

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  3. If x=acos^30theta,y=bsin^30theta, find dy/dx.

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  4. If y=e^(x^(e^x)), find dy/dx.

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  5. If x^y+y^x=1, find dy/dx.

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  6. If e^x+e^y=e^(x+y), find dy/dx.

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  7. If x^yy^x=1, find dy/dx.

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  8. Find the derivative of tan^-1 (sqrt(1-x^2)/x)with respect to cos^-1x .

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  9. Find (d^2y)/(dx^2) if x=a costheta,y=bsintheta.

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  10. If y=e^(ax)sinbx show that y2-2ay1+(a^2+b^2)y=0.

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  11. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

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  12. If u=f((x^2+y^2)/xy) prove that x(partialu)/(partialv)+y(partialu)/(pa...

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  13. If f(x+y)=f(x).f(y) forall x,y and f(5)=2 and f'(0)=3, then show that ...

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  14. If (fog) (1)=3, g(1) = 2, g(1) = 1,then show that f(2)=3.

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  15. If f(a)= 2, f'(a) = 1, g(a)=-1 and g'(a)=2, then find underset(xtoa)li...

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  16. Find the rate of change of the area of circle w.r.t.r when r=8 cm.

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  17. The side of a sqart is increasing at the rate of 0.1 cm//sec and at th...

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  18. A particle moves along a straight line according to the law s=t^3-3t^...

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  19. Show that the function f(x)=1/x is decreasing in (0,oo).

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  20. Find the intervals where the function f(x)=x^3-12x+10 is increasing.

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