find the derivative of ( f(x) ).\n( f(x)=7^{x} )\n( f^{prime}(x)= )
find the derivative of ( f(x) ).\n( f(x)=7^{x} )\n( f^{prime}(x)= )
Answer
Explanation:
Step1: Recall the derivative formula for (a^x)
The derivative of (y = a^x) with respect to (x) is (y'=a^x\ln a) (where (a>0,a\neq1)). In the function (f(x)=7^x), (a = 7).
Step2: Apply the formula
Substitute (a = 7) into the formula (y'=a^x\ln a). So (f'(x)=7^x\ln7).
Answer:
(7^x\ln7)