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" 4."log(e)x^(2)" ."...

" 4."log_(e)x^(2)" ."

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

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Draw and graph of f(x) = (4log_(e)x)/(x^(2)) . Also find the range.

Draw and graph of f(x) = (4log_(e)x)/(x^(2)) . Also find the range.

Draw and graph of f(x) = (4log_(e)x)/(x^(2)) . Also find the range.

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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