1. **State the problem:** Find the derivative of the function $f(x) = 9x^4 + 3x^2 + x + 4$. 2. **Recall the derivative rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant is 0. - The derivative of $x$ is 1. 3. **Apply the power rule to each term:** - Derivative of $9x^4$ is $9 \times 4x^{4-1} = 36x^3$. - Derivative of $3x^2$ is $3 \times 2x^{2-1} = 6x$. - Derivative of $x$ is 1. - Derivative of constant 4 is 0. 4. **Combine all derivatives:** $$f'(x) = 36x^3 + 6x + 1$$ 5. **Final answer:** The derivative of the function is $f'(x) = 36x^3 + 6x + 1$.