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If y=sqrt((1-x)/(1+x)), prove that ((1-x...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If y=x-x^2, then the derivative of y^2 with respect to x^2 is (a)1...

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  19. The first derivative of the function [cos^(-1)(sinsqrt((1+x)/2))+x^x]...

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  20. The function f(x)=e^x+x , being differentiable and one-to-one, has a ...

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