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If x^y = y^x, then dy/dx = ......... A) ...

If `x^y` = `y^x`, then `dy/dx = `......... A) `frac{y(x log y - y)}{x(y log x -x)}` B) `frac{y(y log x - x)}{x(x log y -y)}` C) `frac{y^2 (1- log x)}{x^2 (1- log y)}` D) `frac{y(1- log x)}{x(1-log y)}`

A

`frac{y(x log y - y)}{x(y log x -x)}`

B

`frac{y(y log x - x)}{x(x log y -y)}`

C

`frac{y^2 (1- log x)}{x^2 (1- log y)}`

D

`frac{y(1- log x)}{x(1-log y)}`

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If y= sec (tan^(-1) (x)), then dy/dx at x=1 is equal to ......... A) ...

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  2. If f(x) = sin^(-1){(frac {4^((x +(1/2)))}{1+ 2^(4x)))}, which of the f...

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  3. If x^y = y^x, then dy/dx = ......... A) frac{y(x log y - y)}{x(y log ...

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  4. If y= sin(2 sin^(-1) x), then dy/dx= ............ A) frac{2-4x^2}{sqr...

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  5. If y= tan^(-1) (frac{x}{1+ sqrt (1 - x^2)}) + sin[ 2tan^(-1) (sqrt ((1...

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  6. If y is a function of x and log(x+y) = 2xy, then the value of y'(0) = ...

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  7. If g is the inverse function of f and f'(x)= frac{1}{1+x^7}, then the ...

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  8. If x sqrt (y+1) + y sqrt (x+1) =0 and x != y then dy/dx=............ A...

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  9. If y= tan^(-1) (sqrt (frac {a-x}{a+x})), where -a < x < a then dy/dx= ...

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  10. If x= a(costheta + sintheta), y= a(sintheta + costheta), then (d^2y)/(...

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  11. If y= a cos(log x) and A ((d^2 y)/(dx^2)) + B (dy/dx) + C = 0 , then ...

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  12. If x^y = e^(x-y), then dy/dx = ............ A) frac{1 + x}{1+ log x} ...

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  13. If y= 1- cos theta, x= 1- sin theta, then dy/dx at theta = pi /4 is......

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  14. If sec(frac{x+y}{x-y}) = a^2, then (d^2 y)/(dx^2) = ............ A) y...

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  15. If y = sec^(-1) (frac{sqrt x - 1}{x+sqrt x}) + sin^(-1) (frac{x + sqr...

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  16. Derivative of tan^3theta with respect to sec^3theta at theta = (pi/3) ...

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  17. If x^5y = (x+y)^(n-2) and dy/dx = y/x, then n=..........

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  18. If x= e^2log(e)(sin theta), y= e^2log(e)(cos theta), then dy/dx at ...

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  19. If y= sqrt (log x + sqrt (log x + sqrt (log x + .......oo))), then dy/...

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  20. If y= 5^(2log(5)(sin x)) + 7^(2log(7)(cos x)), then dy/dx= A) 1 B) -...

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