Question

Find the derivative of f(x) = 6x + 2 at x = 1.

Answer 1

`f'(x_0)=\lim\limits_(x\to x_0)(f(x)-f(x_0))/(x-x_0)\\\\f(x)=6x+2;\ x_0=1\\\\f'(1)=\lim\limits_(x\to x_0)((6x+2)-(6\cdot1+2))/(x-1)=\lim\limits_(x\to x_0)(6x+2-8)/(x-1)\\\\=\lim\limits_(x\to x_0)(6x-6)/(x-1)=\lim\limits_(x\to x_0)(6(x-1))/(x-1)=\lim\limits_(x\to x_0)6=6\\\\\\Answer:\boxed{f'(1)=6}`

Answer 2

6

Explanation:

Looking for the derivative of a function is similar to differentiating the function.

Given the function f(x) = 6x+2

The derivative of the function

f'(x) = 6

The derivative of the function at x= 1 will still be equivalent to 6 since 6 is just a constant.