If `f(x)=|{:(2^(-x),e^(x log_(e)2),x^(2)),(2^(-3x),e^(3x log_(e)2),x^(4)),(2^(-5x),e^(5x log_(e)2),1):}| ` then show that `f(x)` is symmetric about origin

" If " g(x) = |{:(a^(-x),,e^(x log _(e)a),,x^(2)),(a^(-3x),,e^(3x log_(e)a),,x^(4)),(a^(-5x),,e^(5x log _(e)a),,1):}| then

If g(x)=|a^(-x)e^(x log_e a)x^2a^(-3x)e^(3x log_e a)x^4a^(-5x)e^(5x log_e a)1| , then graphs of g(x) is symmetrical about the origin graph of g(x) is symmetrical about the y-axis ((d^4g(x))/(dx^4)|)_(x=0)=0 f(x)=g(x)xxlog((a-x)/(a+x)) is an odd function

If f(x)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))} , then f'( e )

If log_(e)x>(x-2)/(x) then x in

If f(x)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))}, then f'((1)/( e )) is equal to

Find the range of f(x)=(log)_(e)x-(((log)_(e)x)^(2))/(|(log)_(e)x|)

If f(x)=log_(x^(3))(log x^(2)), then f'(x) at x=e is

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

int(e^(3log_e(2x))+5e^(2log_e(2x)))/(e^(4log_e(x))+5e^(3log_e(x))-7e^(2log_e(x)))*dx , xgt0

Evaluate: int(e^(5)(log)_(e)x-e^(4)(log)_(e)x)/(e^(3)(log)_(e)x-e^(2)(log)_(e^(x))x)dx