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If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, ...

If `x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2,` then `x^3y (dy)/(dx)=`
(a) `0` (b) `1`(c) `-1` (d) none of these

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  2. y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)),...

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  3. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 ...

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  4. Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

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  5. If e^y(x+1)=1, show that (d^2y)/(dx^2)=((dy)/(dx))^2

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  6. If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((...

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  7. If y=cos^(-1)(cosx),then (dy)/(dx) at x=(5pi)/4 is equal to (a)1 (b)-...

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  8. If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x=(5pi)/4 is equal to (a) 1 (b...

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  9. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a...

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  10. If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt...

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  11. If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/...

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  12. The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a)0 (b) (-1)(...

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  13. If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

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  14. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

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  15. Differentiate x^2+\ 1 with respect to x .

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  16. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  17. Given y= Sin 2x + x^3 , (dy)/(dx)

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  18. Find the derivative of f(x)=e^(4x) + Cos 3x

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  19. A nonzero polynomial with real coefficient has the property that f(x)=...

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  20. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f''(x)-2f^(prime)...

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