find the derivative of ( f(x) ).\n\n( f(x)=2^{x}+e^{x} )\n\n( f^{prime}(x)= )

Explanation:

Step1: Differentiate (2^x)

Use the formula (\frac{d}{dx}(a^x)=a^x\ln a). For (a = 2), (\frac{d}{dx}(2^x)=2^x\ln 2)

Step2: Differentiate (e^x)

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

Step3: Sum the derivatives

By the sum rule ((u + v)'=u'+v'), where (u = 2^x) and (v=e^x). So (f'(x)=2^x\ln 2+e^x)

Answer:

(2^x\ln 2 + e^x)