Find the derivative of f(x)= 3^x-1?

Question

im pretty sure this is logrithmic differentiation, but i can't do it. any help would be appreciated. thanks

Answer 1

I am assuming you just need 3^x?

d/dx(3x)=d/dx(eloge3x)
=d/dx(exloge3)
=(exloge3).loge3
=3x.loge3

Here is a general form for you in case you were looking for:
3^(x-1)

d/dx a^x = ln(a) * a^x. (so just add the ln(a) and multiply by what you already had)

Answer 2

Recall that the derivative of f(x) = a^x is equal to (a^x)(lna). This is true for *ANY* base a. Therefore, if

f(x) = 3^x - 1, then
f'(x) = (3^x)ln(3)

If, however, you meant

f(x) = 3^(x - 1) {all of x - 1 is in the power}
f'(x) = [3^(x - 1)] [ln(3)]

Answer 3

the differentiation for this is :
3^x ln(3)
as diff for a^x is a^x ln(a).