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Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt...

Let `y=x^3-8x+7a n dx=f(t)dot` If `(dy)/(dt)=2` and `x=3` at `t=0,` then `(dx)/(dt)` at `t=0` is given by 1 (b) `(19)/2` (c) `2/(19)` (d) none of these

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RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If a x^2+2h x y+b y^2=0, then (dy)/(dx) is equal to y/x (b) x/y (c) ...

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  2. If f(x)=(log)x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e ...

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  3. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

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  4. Let g is the inverse function of fa n df^(prime)(x)=(x^(10))/((1+x^2))...

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  5. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

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  6. If u=f(x),v=g(x), then the value of D^*(udotv) is (D^*u)v+(D^*v)u b. u...

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  7. Let f(x)={((x-4)/(|x-4|)+a ,x<4),(a+b ,x=4),((x-4)/(|x-4|)+b ,x >4):} ...

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  8. If f(x)=x^3+bx^2+cx+d and 0 < b^2 < c, then in (-oo,oo), (a) f(x) is...

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  9. The point(s) of minimum of function, f(x)=4x^3-x|x-2|,x in [0,3] is x=...

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  10. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive func...

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  11. Let f:(-1,1)vecR be a differentiable function with f(0)=-1 and f^(prim...

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  12. If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(d...

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  13. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

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  14. If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

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  15. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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  16. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)),w h e r eprod(i=1)^k ai st...

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  17. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

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  18. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)...

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  19. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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  20. Find (dy)/(dx) in each of the following cases: y=tan^(-1)(4x)/(1+5x^2...

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