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If xsqrt(1+y)+ysqrt(1+x)=0, prove that d...

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

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If y=sqrt(sinx+sqrt(sinx+sqrt(sin+...oo))), find dy/dx

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  2. If ysqrt(1-x^2)+xsqrt(1-y^2)=1 when |x|lt1 and |y|lt1 find dy/dx

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

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  4. If e^x+e^y=e^(x+y), prove that dy/dx=-e^(y-x)

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  5. Differentiate x^(sin^(-1)x) w.r.t 'x'

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  6. If y= (x)^cosx,find dy/dx

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  7. If x^y=e^(x-y), Prove that dy/dx=logx/(1+logx)^2

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  8. If y=e^(x+e^(x+e^(x+....TOoo))) prove that dy/dx=y/((1-y))

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  9. Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

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

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

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  12. If x=a(theta+sin theta) and y=a(1-costheta), find (d^2y)/(dx^2)"at"the...

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  13. A particle moves along the curve y=2/3x^3. Find the points on the curv...

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  14. A man of height 1.6m, walks at a rate of 30m/sec away from a lamp whic...

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  15. Water is leaking from a conical funnel at the rate of 5cm^3//sec. If t...

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  16. Find the approximate value of log(10)10.1 it being given that log10e=0...

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  17. The time T of of oscillation of a simple pendulum of length l is given...

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  18. If in a triangle ABC, the side c and the angle C remain constant while...

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  19. Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

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  20. Find the interval in which f(x)=x^3-3x^2-9x+30 is strictly increasing ...

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