find the derivative of ( f(x) ).\n( f(x)=10^{x} )\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n( f(x)=10^{x} )\n( f^{prime}(x)= )
Answer
Explanation:
Step1: Recall the derivative formula for (a^x)
The derivative of (y = a^x) is (y^\prime=a^x\ln a), where (a>0,a\neq1). In the function (f(x)=10^x), (a = 10).
Step2: Apply the formula
Substitute (a = 10) into the formula (f^\prime(x)=a^x\ln a). So (f^\prime(x)=10^x\ln10).
Answer:
(10^x\ln10)