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

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

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If y = sqrt(1+sqrt(1+x^4)), prove that y(y^2-1)dy/dx = x^3

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  2. If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...

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

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  4. If cos^(-1)((x^(2)-y^(2))/(x^(2)-y^(2)))=tan^(-1)a, then prove that (d...

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  5. If x^2 + y^2 = t + 1/t and x^4 + y^4 = t^2 + 1/t^2, then show that dy/...

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  6. If log sqrt(x^2 + y^2) = tan^-1 (y//x), then show that dy/dx = (x+y)/(...

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  7. If sqrt(x^2 +1) y = log(sqrt(x^2+1)-x), then show that (x^2 +1) dy/dx ...

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

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  9. If sqrt(1-x^6)+sqrt(1-y^6)=a^3(x^3-y^3), prove that : dy/dx = x^2/y^2s...

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  10. If y = sqrt(x+ sqrt(x + sqrt(x + ......oo))), show that (2y - 1) (dy)/...

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  11. y = sqrt(tan x + sqrt(tanx + sqrt(tanx + ...."to" oo))) prove that (2y...

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  12. Differentiate the following functions w.r.t.x : (x+1)^2 (x+2)^3 (x+3)^...

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  13. Differentiate the following functions w.r.t.x : sqrt((x-1)(x-2)(x-3)(x...

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  14. Differentiate the following functions w.r.t.x : e^x cos^3 x sin^4 x

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  15. Differentiate the following functions w.r.t.x : x^2 e^x sin x

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  16. Differentiate the following functions w.r.t.x : (2x+1)^(1//2) (3x +2)^...

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  17. Differentiate the following functions w.r.t.x : e^x cos^3 x sin^4 x

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  18. Differentiate the following w.r.t. x : cos x . Cos 2x. Cos 3x

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  19. Differentiate the following w.r.t. x: (sinx)^(cos^-1x)

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  20. Find (dy)/(dx) when x^y + y^x = a^b

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