find the derivative of ( f(x) ).\n\n( f(x)=9^{x} )\n\n( f^{prime}(x)= )

Explanation:

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

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

Step2: Identify (a) in the function (f(x)=9^x)

Here (a = 9).

Step3: Apply the formula

Substitute (a = 9) into the formula (y'=a^x\ln a). So (f'(x)=9^x\ln9).

Answer:

(9^x\ln9)