find the derivative of ( f(x) ).\n\n( f(x)=8^{x}-e^{x} )\n\n( f^{prime}(x)= )

Explanation:

Step1: Differentiate (8^x)

Use the formula (\frac{d}{dx}(a^x)=a^x\ln a), so (\frac{d}{dx}(8^x)=8^x\ln 8)

Step2: Differentiate (-e^x)

Use the formula (\frac{d}{dx}(e^x)=e^x), so (\frac{d}{dx}(-e^x)=-e^x)

Step3: Combine the derivatives

By the sum - difference rule ((u - v)'=u'-v'), where (u = 8^x) and (v=e^x). Then (f'(x)=\frac{d}{dx}(8^x)-\frac{d}{dx}(e^x))

Answer:

(8^x\ln 8 - e^x)