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If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(d...

If `y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s` (a) `(-1)/(2|x|sqrt(x^2-1))` (b) `(-1)/(2xsqrt(x^2-1))` (c) `1/(2xsqrt(x^2-1))` (d) none of these

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. 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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  2. 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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  3. 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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  4. If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/...

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

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

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

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

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

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

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

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

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

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  14. Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(...

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  15. A function is reprersented parametrically by the equations x=(1+t)/(t^...

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  16. Let f be a twice differentiable function such that f^(prime prime)(x)=...

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  17. Let y=e^(x sin x^3)+(t a n x)^x Find (dy)/(dx)

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  18. If a x^2+2h x y+b y^2=1,t h e n(d^2y)/(dx^2) is (a)(h^2-a b)/((h x+b...

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  19. If y=sinp x and yn is the n t h derivative of y , then |[y, y1,y2],[y3...

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  20. A function f, defined for all positive real numbers, satisfies the eq...

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