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If a>0, x=(t+1/t)^a ,y=a^(t+1/t),"find "...

If `a>0`, `x=(t+1/t)^a ,y=a^(t+1/t),"find " (dy)/(dx)`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function from first principles: x^2e^x

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  2. Differentiate the function (logsinx)^2 with respect to x

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  3. If a>0, x=(t+1/t)^a ,y=a^(t+1/t),"find " (dy)/(dx)

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  4. If x=a((1+t^2)/(1-t^2))"and"y=(2t)/(1-t^2),"f i n d"(dy)/(dx)

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  5. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), show that at pi/4,(dy)/...

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

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  7. If x=3sint-sin3t ,y=3cos t-cos3t ,"find "(dy)/(dx)" at "t=pi/3dot

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

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

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

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

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

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  13. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

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  14. If sin^-1x+sin^-1y+sin^-1z=(3pi)/2, then find the value of x^2+y^2+z^2

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

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  16. 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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  17. 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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  18. If y=sqrt(sinx+y) then (dy)/(dx)= (a) (sinx)/(2y-1) (b) (sinx)/(1-2y)...

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  19. 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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  20. If sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)i se q u a lto ...

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