Differentiate the following with respect to x:

e^{x log a} + e^{a log x} + e^{a log a}

Given,

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

⇒ f(x) =

We know that, e^{log f(x) =} f(x)

∴ f(x) = a^x + x^a + a^a

we need to find f’(x), so differentiating both sides with respect to x –

∴

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = a^x log_e a – ax^{a – 1} + 0

⇒ f’(x) = a^x log_e a – ax^{a – 1}