1. The problem is to find the derivatives (Ableitung) of the two given functions: - $f(x) = 4x^3 - 2x + 1$ - $f(x) = \frac{1}{x^4}$ 2. For the first function $f(x) = 4x^3 - 2x + 1$, apply the power rule to each term: - Derivative of $4x^3$ is $4 \times 3x^{3-1} = 12x^2$ - Derivative of $-2x$ is $-2$ - Derivative of constant $1$ is $0$ So, $f'(x) = 12x^2 - 2$ 3. For the second function $f(x) = \frac{1}{x^4}$, rewrite it as $f(x) = x^{-4}$ to use the power rule: - Derivative is $-4x^{-5} = -\frac{4}{x^5}$ 4. Final answers: - $f'(x) = 12x^2 - 2$ - $f'(x) = -\frac{4}{x^5}$