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If x^y=e^(x-y), Prove that (dy)/(dx)=(lo...

If `x^y=e^(x-y),` Prove that `(dy)/(dx)=(logx)/((1+logx)^2)`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

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  2. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

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

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  4. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

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  5. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

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  6. If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value...

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  7. If x y+y^2=tanx+y ,then find (dy)/(dx)

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  8. Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e...

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  9. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+oo)))),t h e np rov et h a t(dy)/(dx)...

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  10. If y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a)y/x(1n x^(x-...

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  11. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(c...

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  12. The n t h derivative of x e^x vanishes when (a)x=0 (b) x=-1 (c)...

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  13. If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

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  14. The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)...

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  15. If x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot

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  16. Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on...

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  17. If x=acos^3theta,y=a sin^3theta,then find the value of d2y/dx2 at θ=π/...

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  18. If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t) , a >0 a n d -1 < t...

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  19. If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1, then find the...

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  20. If y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2, then find (dy)/(dx)

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