find the derivative of ( f(x) ).\n\n( f(x)=5^{x} )\n\n( f^{prime}(x)= )

Explanation:

Step1: Recall the derivative formula for (a^x)

The derivative of (y = a^x) is (y'=a^x\ln a), where (a>0,a\neq1).

Step2: Identify (a) in the given function

In the function (f(x)=5^x), (a = 5).

Step3: Apply the formula

Substitute (a = 5) into the formula (f'(x)=a^x\ln a). So (f'(x)=5^x\ln 5).

Answer:

(5^x\ln 5)