Question

Find the derivative: f(x) =2x-4

Answer 1

To find the derivative of the function f(x) = 2x - 4 with respect to x, you can use the power rule of differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). In this case, the function is already in a simple linear form, so the derivative is straightforward:

f'(x) = d/dx (2x - 4)

Using the power rule:

f'(x) = 2 * 1 * x^(1-1) - 0

Simplify:

f'(x) = 2 * x^0

Any non-zero number raised to the power of 0 is 1, so:

f'(x) = 2 * 1

f'(x) = 2

So, the derivative of f(x) = 2x - 4 is f'(x) = 2.

Answer 2

f'(x) = 2

Explanation:

The derivative of a function is the measure of how quickly the function is changing at a given point. It is calculated using the following formula:

`\sf f'(x) = lim_(h \to 0) (f(x + h) - f(x))/( h)`

where f(x) is the function and f'(x) is the derivative of the function at the point x.

To find the derivative of the function f(x) = 2x - 4, we can use the following steps:

Substitute the function into the derivative formula.

`\sf f'(x) = lim_(h \to 0) ((2(x + h) - 4) - (2x - 4))/(h)`

Simplify the expression.

`\sf f'(x) = lim_(h \to 0) (2x + 2h - 4 - 2x + 4)/( h)`

`\sf f'(x) = lim_(h \to 0) (2h)/(h)`

`\sf f'(x) = lim_(h \to 0) 2`

Take the limit as h approaches 0.

f'(x) = 2

Therefore, the derivative of the function f(x) = 2x - 4 is 2.