1. **State the problem:** Differentiate the function $$y = 7x^5 - 4x^3 + 9x - 2$$ with respect to $$x$$. 2. **Recall the power rule for differentiation:** If $$y = x^n$$, then $$\frac{dy}{dx} = nx^{n-1}$$. 3. **Apply the power rule to each term:** - For $$7x^5$$, derivative is $$7 \times 5x^{5-1} = 35x^4$$. - For $$-4x^3$$, derivative is $$-4 \times 3x^{3-1} = -12x^2$$. - For $$9x$$, derivative is $$9 \times 1x^{1-1} = 9$$. - For constant $$-2$$, derivative is $$0$$. 4. **Combine all derivatives:** $$\frac{dy}{dx} = 35x^4 - 12x^2 + 9$$ **Final answer:** $$\boxed{\frac{dy}{dx} = 35x^4 - 12x^2 + 9}$$