Question

find the derivative of ( f(x) ).

( f(x)=5^{x} )

( 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 \(a>0,a
eq1\).

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:

\(5^x\ln 5\)