Question: Find the derivative of the following function. yequalsnegative 5 x squared plus 7 cosine x
StartFraction dy Over dx EndFraction equals enter your response here
1. **State the problem:** Find the derivative of the function $$y = -5x^2 + 7\cos x$$.
2. **Recall the derivative rules:**
- The derivative of $$x^n$$ is $$nx^{n-1}$$.
- The derivative of $$\cos x$$ is $$-\sin x$$.
- The derivative of a constant times a function is the constant times the derivative of the function.
3. **Apply the derivative:**
$$\frac{dy}{dx} = \frac{d}{dx}(-5x^2) + \frac{d}{dx}(7\cos x)$$
4. **Differentiate each term:**
- For $$-5x^2$$: $$\frac{d}{dx}(-5x^2) = -5 \cdot 2x^{2-1} = -10x$$
- For $$7\cos x$$: $$\frac{d}{dx}(7\cos x) = 7 \cdot (-\sin x) = -7\sin x$$
5. **Combine the results:**
$$\frac{dy}{dx} = -10x - 7\sin x$$
**Final answer:**
$$\boxed{\frac{dy}{dx} = -10x - 7\sin x}$$