**Calculus - Chain Rule Application**### Problem StatementUse the chain rule to find the derivative of:\[ 5\left( -5x^4 - 8x^3 \right)^{14} \]You do not need to expand out your answer.### SolutionTo tackle this problem, first identify the outer and inner functions for applying the chain rule. Here's a structured approach:1. **Outer Function (u)**: \( u = 5z^{14} \) 2. **Inner Function (z)**: \( z = -5x^4 - 8x^3 \)3. **Derivative of Outer Function \( \frac{du}{dz} \)**: \[ \frac{d}{dz}(5z^{14}) = 5 \cdot 14z^{13} = 70z^{13} \] 4. **Derivative of Inner Function \( \frac{dz}{dx} \)**: \[ \frac{d}{dx}(-5x^4 - 8x^3) = -20x^3 - 24x^2 \]5. **Combine Using Chain Rule**: \[ \frac{du}{dx} = \frac{du}{dz} \cdot \frac{dz}{dx} \] Substituting back the inner function (z): \[ \frac{du}{dx} = 70(-5x^4 - 8x^3)^{13} \cdot (-20x^3 - 24x^2) \]This is your final result. Remember, it is not necessary to simplify further unless explicitly required.

Name: **Calculus - Chain Rule Application**### Problem StatementUse the cha
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: **Calculus - Chain Rule Application**### Problem StatementUse the chain rule to find the derivative of:\[ 5\left( -5x^4 - 8x^3 \right)^{14} \]You do not need to expand out your answer.### SolutionTo tackle this problem, first identify the outer and