Question

If f(x) = 2x-6x, then f'(x) is

Answer 1

-4

Answer 2

The given function is $f(x) = 2x - 6x$.

First, simplify the function $f(x)$:

$$f(x) = (2 - 6)x$$ $$f(x) = -4x$$

Now, find the derivative of $f(x)$ with respect to $x$. The derivative of a term $cx$ (where $c$ is a constant) is simply $c$. Using the power rule for differentiation, $\frac{d}{dx}(x^n) = nx^{n-1}$:

$$f'(x) = \frac{d}{dx}(-4x)$$ $$f'(x) = -4 \cdot \frac{d}{dx}(x^1)$$ $$f'(x) = -4 \cdot (1 \cdot x^{1-1})$$ $$f'(x) = -4 \cdot (1 \cdot x^0)$$

Since $x^0 = 1$ (for $x \neq 0$),

$$f'(x) = -4 \cdot 1$$ $$f'(x) = -4$$