### Calculus: Derivatives Practice Problems#### Problem 1:**Find the derivative of:**\[ -5x^8 - 2x^4 - 8x - 2 \]\[\frac{d}{dx} \left( -5x^8 - 2x^4 - 8x - 2 \right) = \boxed{\phantom{\text{Type your answer here.}}}\]---#### Problem 2:**Find the derivative of:**\[ -8 \sqrt[4]{x} + \frac{3}{x^5} + 7x + 9 \]\[\frac{d}{dx} \left( -8 \sqrt[4]{x} + \frac{3}{x^5} + 7x + 9 \right) = \boxed{\phantom{\text{Type your answer here.}}}\]---**Question Help:**- [Video](#) - [Written Example](#)**Add Work:**- [Add Work](#)---### Explanation:1. **First Problem: Differentiating a Polynomial** To differentiate the polynomial \(-5x^8 - 2x^4 - 8x - 2\), apply the power rule: \[ \frac{d}{dx} \left( ax^n \right) = nax^{n-1}. \] - For \(-5x^8\), the derivative is \( -5 \cdot 8x^{7} = -40x^7 \). - For \(-2x^4\), the derivative is \(-2 \cdot 4x^3 = -8x^3 \). - For \(-8x\), the derivative is \(-8 \cdot 1x^0 = -8\). - The constant \(-2\) has a derivative of \(0\). Putting it all together: \[ \frac{d}{dx} \left( -5x^8 - 2x^4 - 8x - 2 \right) = -40x^7 - 8x^3 - 8 \]2. **Second Problem: Differentiating a Sum of Functions** To differentiate the sum \(-8 \sqrt

Name: ### Calculus: Derivatives Practice Problems#### Problem 1:**Find the
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Description: ### Calculus: Derivatives Practice Problems#### Problem 1:**Find the derivative of:**\[ -5x^8 - 2x^4 - 8x - 2 \]\[\frac{d}{dx} \left( -5x^8 - 2x^4 - 8x - 2 \right) = \boxed{\phantom{\text{Type your answer here.}}}\]---#### Problem 2:**Find the deriv