1. **State the problem:** Differentiate the function $y=7x^3 - 5x^2$ with respect to $x$. 2. **Recall the differentiation rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant times a function is the constant times the derivative of the function. 3. **Apply the power rule to each term:** - For $7x^3$, derivative is $7 \times 3x^{3-1} = 21x^2$. - For $-5x^2$, derivative is $-5 \times 2x^{2-1} = -10x$. 4. **Combine the derivatives:** $$\frac{dy}{dx} = 21x^2 - 10x$$ 5. **Final answer:** The derivative of the function $y=7x^3 - 5x^2$ is $$\boxed{\frac{dy}{dx} = 21x^2 - 10x}$$