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If y=tan^(-1)(1/(1+x+x^2))+tan^(-1)(1/(x...

If `y=tan^(-1)(1/(1+x+x^2))+tan^(-1)(1/(x^2+3x+3))+tan^(-1)(1/(x^2+5x+7))++` upto `n` terms, then find the value of `y^(prime)(0)dot`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) for the functions: y=x^3e^xsinx

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  2. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b)...

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  3. If y=tan^(-1)(1/(1+x+x^2))+tan^(-1)(1/(x^2+3x+3))+tan^(-1)(1/(x^2+5x+7...

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  4. Let g(x) be the inverse of an invertible function f(x) which is diff...

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  5. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2...

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  6. Let f: R->R be such that f(1)=3 and f^(prime)(1)=6. Then lim(x->0)((f...

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

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  8. Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]|, where p is a cons...

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  9. Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

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  10. The derivative of an even function is always an odd function.

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  11. If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e n d(dy)/...

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  12. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) a...

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  13. Find (dy)/(dx) for y=tan^(-1){(1-cosx)/(sinx)},-piltxltpi.

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  14. If x=y+sin^2x then at x=0 ,(dy)/dx=

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  15. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x.

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  16. If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= for x>20

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  17. Find (dy)/(dx) for y=tan^(-1) sqrt(sec^2x/ cosec^2x)

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  18. If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a)(sinx)^(tanx)(1+sec^2xlogsi...

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  19. If y=sin^(-1)(sqrt(1-x^2]) and 0 < x < 1, then find (dy)/(dx)

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  20. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

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