How do you find the derivative of f(x)=7^(2x)?

1 Answer
Apr 3, 2018

ln49[7^[2x]]

Explanation:

By the theory of logs 7^[2x can be written as e^[2xln7] ,i.e,

7^[2x]=e^[2xln7].....[1]

Therefore, d/dx7^[2x= d/[dx][e^[2xln7]]

d/dx[e^[2xln7]]=[e^[2xln7]d/dx[2xln7]] and since ln7 is a constant,

d/dx[2xln7] = 2ln7..... So, d/dx7^[2x=2ln7[e^[2xln7]].......[2]

From .....[1], e^[2xln7= 7^[2x so substituting in 2,

d/dx 7^[2x=2ln7[7^[2x]]=ln49[7^[2x]]. Hope this was helpful.