Question

If f(x) = ex and g(x) = loge x, then (gof)’ (x) is​

Answer 1

$\large\rm { f(x) = e^{x}}$

$\large\rm{ g(x) = e^{ln \ x}}$

$\large\rm { f \circ g = x}$

$\large\rm { \therefore g \circ f = x}$

Answer 2

Step-by-step explanation:

$\implies \: f(x) = {e}^{x} \\ \\ \implies \: g(x) = \log_{e}(x) \\ \\ \implies \red{gof = g(fx)} \\ \\ \implies \: gof = g( {e}^{x} ) \\ \\ \implies \: g( {e}^{x} ) = \log_{e}( {e}^{x} ) \\ \\ \implies \boxed{\pink{ \log \: {m}^{n} = n \log \: m }} \: \\ \\ \implies \boxed{ \pink{ log_{e}(e) = 1}} \\ \\ \implies \: g( {e}^{x} ) = x \log_{e}(e) \\ \\ \implies \: gof = x$

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