find the derivative of $f(x)$.\n$f(x)=e^{x}-4^{x}$\n$f^{prime}(x)=$
find the derivative of $f(x)$.\n$f(x)=e^{x}-4^{x}$\n$f^{prime}(x)=$
Answer
Explanation:
Step1: Differentiate (e^x)
The derivative of (e^x) with respect to (x) is (e^x).
Step2: Differentiate (4^x)
Using the formula (\frac{d}{dx}(a^x)=a^x\ln a) (where (a = 4)), the derivative of (4^x) is (4^x\ln 4).
Step3: Apply the difference rule
If (f(x)=u(x)-v(x)), then (f^\prime(x)=u^\prime(x)-v^\prime(x)). Here (u(x)=e^x), (u^\prime(x)=e^x) and (v(x)=4^x), (v^\prime(x)=4^x\ln 4). So (f^\prime(x)=e^x - 4^x\ln 4).
Answer:
(e^x-4^x\ln 4)