find the derivative of ( f(x) ).\n\n( f(x)=e^{x}-10^{x} )\n\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n\n( f(x)=e^{x}-10^{x} )\n\n( f^{prime}(x)= )
Answer
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 (10^x)
Use the formula (\frac{d}{dx}(a^x)=a^x\ln a). For (a = 10), (\frac{d}{dx}(10^x)=10^x\ln 10).
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)=10^x), (v^{\prime}(x)=10^x\ln 10). So (f^{\prime}(x)=e^x - 10^x\ln 10).
Answer:
(e^x-10^x\ln 10)