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If x^p y^q= (x+y)^(p+q), then prove that...

If `x^p y^q= (x+y)^(p+q)`, then prove that `dy/dx = y/x`

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If x= a(t-(1/t)), y=a(t+(1/t)), then show that dy/dx = x/y

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  2. If sqrt (1-x^2) + sqrt (1-y^2) = a(x-y), show that dy/dx = sqrt (frac...

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  3. If x^p y^q= (x+y)^(p+q), then prove that dy/dx = y/x

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

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  5. If log(10)(frac{x^3 -y^3}{x^3+y^3}) =2, then show that dy/dx = (-99x^2...

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  6. Differentiate: cos^(-1) frac{3cos x - 2 sin x}{sqrt 13} w.r.t. x

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  7. If y=cos^(-1) (2x sqrt (1-x^2)), find dy/dx

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  8. If y= e^(tan x) + (log x)^(tan x), then find dy/dx

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  9. Find dy/dx, if y= tan^(-1) frac{3a^2x - x^3}{a^3 - 3a x^2}

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  10. If sec^(-1) (frac {x+y}{x-y}) = a^2, show that dy/dx = y/x

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  11. Find dy/dx, if y= tan^(-1) frac{3a^2x - x^3}{a^3 - 3a x^2}

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  12. If x= afrac{1-t^2}{1+t^2}, y= 2bt/(1+t^2), show that dy/dx = -(b^2 y)/...

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  13. If y= log(x+ sqrt (x^2 + a^2)), show that (x^2 + a^2)(d^2 y)/(dx^2) + ...

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  14. If ax^2 + 2hxy + by^2 =0, show that (d^2 y)/(dx^2) = y/x

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  15. If x= a cos theta, y= b sin theta, show that a^2[y (d^2 y)/(dx^2) +(dy...

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  16. If y= cos (m sin^(-1) x), show that (1- x^2)(d^2 y)/(dx^2) - x(dy/dx) ...

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  17. If x= cos theta, y= sin^3theta, show that y (d^2 y)/(dx^2) + (dy/dx)^2...

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  18. If 2y= sqrt (x+1) + sqrt (x-1), show that 4(x^2 -1) y2 + 4xy1 - y = 0

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  19. Find dy/dx if y= log (frac { x+ sqrt (x^2+a^2) }{sqrt (x^2+a^2) - x ...

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  20. Let f(1)=3, f'(1)= frac{-1}{3}. g(1)=-4, and g'(1) = frac{-8}{3}, The ...

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