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If siny=xsin(a+y), prove that (dy)/(dx)=...

If `siny=xsin(a+y),` prove that `(dy)/(dx)=(sin^2(a+y))/(sina)`

A

`(sin^2(a+y))/(sin(a+y))`

B

`(sin^2(a+y))/(cos(a+2y))`

C

`(sin^2(a+y))/(sina)`

D

`(sin^2(a+y))/(cosa)`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. IF log (10)""((x^(3)-y^(3))/(x^(3)+y^(3)))=2 then (dy)/(dx)=

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  2. cos^(- 1)((x^2-y^2)/(x^2+y^2))=loga find dy/dx

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  3. If siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  4. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y))/(...

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  5. If sin (xy) + (x)/(y) =x^(2) - y , " then " (dy)/(dx) is equal to

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  6. If ysqrt(x^2+1)=log{sqrt(x^2+1)-x} , then (x^2+1)(dy)/(dx)+x y+1 is eq...

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  7. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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  8. if 2^x+2^y=2^(x+y) then the value of (dy)/(dx) at x=y=1

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  9. If siny+e^(-xcosy)=e, then (dy)/(dx) at (1,pi), is

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  10. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0....

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  11. The dIfferential coefficient of x^6 with respect to x^3 is

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  12. Darivative of sin x w.r.t. cos x is

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  13. The derivative of sin^2x with respect to cos^2x is equal to....

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  14. The derivative of cos^(3)x w.r.t. sin^(3)x is

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  15. The derivative of log(10x) with respect to x^(2), is

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  16. The dIfferential coefficient of log10 x with respect to logx 10 is

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  17. If x=a cos^3theta,y=asin^3theta, then 1+((dy)/(dx))^2 is

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  18. If x = log (1 + t^(2)) " and " y = t - tan^(-1)t, " then" dy/dx is e...

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  19. If x=a(t-sint), y=a(1-cost), then (dy)/(dx) is equal to

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  20. If x=2 cos theta- cos 2 theta and y=2 sin theta - sin 2 theta, then (d...

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