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"If "xsqrt(1+y)+ysqrt(1+x)=0," prove tha...

`"If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).`

A

`(1)/((1+x)^(2))`

B

`-(1)/((1+x)^(2))`

C

`(1)/(1+x^(2))`

D

`(1)/(1-x^(2))`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
  1. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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  2. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

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

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  4. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  5. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  6. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

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  7. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

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  8. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

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  9. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

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  10. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

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  11. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

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  12. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  13. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

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  14. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

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  15. If y=logu|cos4x|+|sinx|,where u=sec2x find (dy)/(dx) at x=-pi/6

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  16. If f(4)= 4, f'(4) =1 then lim(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is ...

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  17. if 2x^2-3xy+y^2+x+2y-8=0 then (dy)/(dx)

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  18. If y=log{((1+x)/(1-x))^(1//4)}-(1)/(2)tan^(-1)x," then "(dy)/(dx)=

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  19. If x=costheta,y=sin5theta," then "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx...

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  20. If f : R - R is an even function which is twice differentiable on R an...

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