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If x=3sint-sin3t ,y=3cos t-cos3t ,"f i n...

If `x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot`

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To find \(\frac{dy}{dx}\) at \(t = \frac{\pi}{3}\), we will follow these steps: ### Step 1: Find \(\frac{dy}{dt}\) Given: \[ y = 3\cos t - \cos 3t \] ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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  2. If x=(1+logt)/(t^2),y=(3+2logt)/t ,"f i n d"(dy)/(dx)dot

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  3. If x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot

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  4. If sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot

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  5. Differentiate tan^(-1)((cosx)/(1+sinx)) with respect to sec^(-1)...

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

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  7. If f(x)=(log)(x^2)(logx), then f^(prime)(x) at x=e is 0 (b) 1 (c) 1...

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  8. The derivative of the function cot^(-1){(cos2"x")^(1/2)}a tx=pi/6 is (...

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  9. If f(x),g(x)and h(x) are three polynomials of degree 2, then prove tha...

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  10. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...

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  11. If 3sin(x y)+4cos(x y)=5 then dy/dx=

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  12. If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l), the...

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  13. d/(dx){tan^(-1)((cosx)/(1+sinx))}e q u a l 1/2 (b) x (c) (1-x^2)/(1...

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  14. Ify=sqrt(sinx+y ,) then (dy)/(dx)= (sinx)/(2y-1) (b) (sinx)/(1-2y) ...

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  15. If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)...

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  16. If sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)is equal to (x^...

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  17. If (1+x)^n=c0+C1x+C2x^2++Cn x^n ,using derivative prove that C1+2...

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  18. Differentiate the following function with respect to x, "tan"(x^0+...

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  19. If y={x+sqrt(x^2+a^2)}^n , then prove that (dy)/(dx)=(n y)/(sqrt((x^2...

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  20. If y=(xsin^(-1)x)/(sqrt(1-x^2))+logsqrt(1-x^2) , then prove that (dy)...

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