1. The problem asks to find the 10th derivative of the function $$h(x) = 3x - 300 + 3^3 + 6x^5$$. 2. First, simplify the constant term: $$3^3 = 27$$, so the function becomes $$h(x) = 3x - 300 + 27 + 6x^5 = 3x - 273 + 6x^5$$. 3. Recall the derivative rules: - The derivative of a constant is 0. - The derivative of $$x^n$$ is $$nx^{n-1}$$. 4. Compute the first derivative: $$h'(x) = \frac{d}{dx}(3x) - \frac{d}{dx}(273) + \frac{d}{dx}(6x^5) = 3 + 0 + 30x^4 = 3 + 30x^4$$. 5. Compute the second derivative: $$h''(x) = \frac{d}{dx}(3) + \frac{d}{dx}(30x^4) = 0 + 120x^3 = 120x^3$$. 6. Compute the third derivative: $$h^{(3)}(x) = \frac{d}{dx}(120x^3) = 360x^2$$. 7. Compute the fourth derivative: $$h^{(4)}(x) = \frac{d}{dx}(360x^2) = 720x$$. 8. Compute the fifth derivative: $$h^{(5)}(x) = \frac{d}{dx}(720x) = 720$$. 9. Compute the sixth derivative: $$h^{(6)}(x) = \frac{d}{dx}(720) = 0$$. 10. Since the sixth derivative and all higher derivatives of a polynomial term of degree 5 are zero, the 10th derivative is also zero: $$h^{(10)}(x) = 0$$. Final answer: $$h^{(10)}(x) = 0$$.