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

If `e^y(x+1)=1`, prove that `(d^2y)/(dx^2)=((dy)/(dx))^2`

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If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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

If ye^(y)=x , prove that, (dy)/(dx)=(y)/(x(1+y)) .

If y=xlog (x/(a+bx)) , prove that x^3(d^2y)/(dx^2)=(y-xdy/dx)^2 .

If y=sin^(-1) x, prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0

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If ye^y=x prove that (dy)/(dx)= y/(x(1+y))

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. 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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  2. Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

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

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  4. y=tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) show that dy/d...

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

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

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  7. 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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  8. 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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  9. If y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2), then (dy)/...

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

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  11. lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0

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

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

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

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

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

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

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  18. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f^(prime prime)(x...

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

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

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