Question

Differentiate
$f(x) = e^{xlog~a} + e^{alog~x}+e^{a log~a}$ ​

Answer 1

Step-by-step explanation:

We have,

$f(x) = {e}^{x log(a) } + {e}^{a log(x) } + {e}^{a log(a) }$

Using properties of log,

$f(x) = {e}^{log(a ^{x} ) } + {e}^{ log(x ^{a} ) } + {e}^{log(a ^{a} ) }$

$f(x) = {a}^{x} + {x}^{a} + {a}^{a}$

Differentiating both sides w.r.t x, we have,

$f^{\prime}(x) = { a}^{x} . ln(a) + a {x}^{a - 1} + 0$

$f^{\prime}(x) = { a}^{x} . ln(a) + a {x}^{a - 1}$