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

If `e^(x)+e^(y)=e^(x+y)`, prove that `(dy)/(dx)+e^(y-x)=0`.

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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. If x^(2)+y^(2)=t-(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)), show that ...

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  2. If ysqrt(x^(2)+1)=log(x+sqrt(x^(2)+1)), show that (x^(2)+1)(dy)/(dx)+x...

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  3. If e^(x)+e^(y)=e^(x+y), prove that (dy)/(dx)+e^(y-x)=0.

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  4. If xsqrt(1+y+)ysqrt(1+x)=0 then (dy)/(dx) equals.

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  5. If y=x^(e^(x^(2))), find (dy)/(dx).

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  6. If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

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  7. Differentiate the following w.r.t.x. If y^x = e^(y - x), prove that ...

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  8. If x^p . y^q = (x + y)^(p + q) , show that (dy)/(dx) = y/x

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  9. If x^16 . y^9 = (x^2 + y)^(17), prove that (dy)/(dx) = (2y)/x.

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  10. Find (dy)/(dx), if y^(x) + x^(y) +x^(x) = a^(b).

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  11. If y=asinx+bcosx, prove thaty^2+((dy)/(dx))^2=a^2+b^2

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

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  13. Find the value of (dy)/(dx) at theta=(pi)/(4) if x=ae^(theta)(sintheta...

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  14. If x=cost(3-2cos^(2)t) and y=sint(3-2sin^(2)t), find the value of (dy)...

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  15. If x=asin2t(1+cos2t)" and "y=bcos2t(1-cos2t). show that ((dy)/(dx))(t=...

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  16. Find (dy)/(dx) at t=(pi)/(4),(pi)/(3), when x=a(cost+log"tan"(t)/(2)),...

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  17. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy...

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  18. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), find (dy)/(dx).

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  19. Find dy/dx when : y = x^(cotx) +(2x^2-3)/(x^2+x+2)

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  20. Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^((1)/(x)).

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