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Differentiate the following w.r.t.x. I...

Differentiate the following w.r.t.x.
If `y^x = e^(y - x)`, prove that `(dy)/(dx) = ((1 + log y)^2)/(log y)`

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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. If y=x^(e^(x^(2))), find (dy)/(dx).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If (cosx)^(y)=(siny)^(x), then find (dy)/(dx).

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  18. If y=x^(cotx)+(sinx)^(x), find (dy)/(dx).

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  19. Differentiate (sinx)^(x)+(cosx)^(sinx) w.r.t. x.

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  20. Differentiate sin^-1(2^(x+1)/(1+4^x)) w.r.t x

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