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If sin (x + y) = y cos (x + y) then prov...

If sin (x + y) = y cos (x + y) then prove that
`dy/dx =-(1 + y^2)/y^2`

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. If y=sin^(-1)[((5x+12(sqrt(1-x^2)))/13)] then find (dy)/(dx).

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  2. If y=tan(x+y), then find (dy)/(dx).

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  3. If y=x^(cotx)+(sinx)^x then find (dy)/(dx).

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  4. If y=(sin^(-1)x)/(sqrt(1-x^(2))), the prove that (1-x^(2))(d^(2)y)/(dx...

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  5. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  6. If y=(log x)^(cos x)+(x^2+1)/(x^2-1) find (dy)/(dx).

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  7. If y= cos^(-1)[(3x+4sqrt(1-x^2))/5] then find (dy)/(dx).

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  8. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  9. Differentiate sin^(-1) (2ax sqrt(1-a^2x^2)) wth respect to sqrt(1-a^2...

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  10. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  11. Find (dy)/(dx) when y= cot^(-1)( cosecx)+(xsin^(-1)x)/(sqrt(1-x^2).

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  12. Find the derivative of ((x-1)/(x^2+5))^-4 cos^-1((1-x^2)/(1+x^2))

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  13. Find (dy)/(dx) when y=tan^(-1)sqrt((1+sinx)/(sinx)).

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  14. Find (dy)/(dx) when (x+y)^(p+q) = x^py^q.

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  15. If x e^(xy)+y=sin^2x, then find (dy)/(dx) at x=0.

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  16. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  17. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  18. Differentiate tan^(-1)((1+sinx)/(1-sinx))^(1/2) with respect to ((1+...

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  19. Find (dy)/(dx) when x=e^(tan^(-1)((y-x^2)/(x^2)).

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  20. If y=x^(sin^(-1x)) + x^3(sqrt(x^2+4)/(sqrt(x^3+3)) then find (dy)/(dx)...

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