1. The problem asks to find the derivative of the function given in the image (assuming the function is $f(x) = x^3 - 5x^2 + 6x - 2$ as a typical calculus-level question). 2. The formula for the derivative of a polynomial function $f(x) = ax^n$ is $f'(x) = n \cdot a x^{n-1}$. 3. Applying the power rule to each term: - Derivative of $x^3$ is $3x^2$. - Derivative of $-5x^2$ is $-10x$. - Derivative of $6x$ is $6$. - Derivative of constant $-2$ is $0$. 4. Combining these results, the derivative is: $$f'(x) = 3x^2 - 10x + 6$$ 5. This derivative function tells us the slope of the original function at any point $x$. Final answer: $$f'(x) = 3x^2 - 10x + 6$$