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

Explanation:

Step1: Differentiate (e^x)

The derivative of (e^x) with respect to (x) is (e^x), i.e., (\frac{d}{dx}(e^x)=e^x).

Step2: Differentiate (2^x)

Using the formula (\frac{d}{dx}(a^x)=a^x\ln a) (where (a = 2)), we get (\frac{d}{dx}(2^x)=2^x\ln 2).

Step3: Apply the difference rule

Since (f(x)=e^x - 2^x), by the difference rule ((u - v)'=u' - v') (where (u = e^x) and (v = 2^x)), we have (f'(x)=\frac{d}{dx}(e^x)-\frac{d}{dx}(2^x)).

Substituting the derivatives from Step1 and Step2: (f'(x)=e^x-2^x\ln 2).

Answer:

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