### Problem StatementGiven the function \( g(x) = \cos(x) \), find the following:1. The derivative of the function \( g'(x) \): \[ g'(x) = \, \underline{\quad \quad} \]2. The value of the derivative at \( x = 1 \): \[ g'(1) = \, \underline{\quad \quad} \]### Explanation and CalculationTo solve this problem, we need to recall the derivative rules for trigonometric functions.**1. Derivative of \( g(x) = \cos(x) \)**The derivative of \( \cos(x) \) is given by:\[g'(x) = -\sin(x)\]Therefore,\[g'(x) = -\sin(x)\]**2. Value of the derivative at \( x = 1 \)**We substitute \( x = 1 \) into the derivative \( g'(x) = -\sin(x) \):\[g'(1) = -\sin(1)\]Thus, the value of the derivative at \( x = 1 \) is \( -\sin(1) \). Note: \( \sin(1) \) is evaluated in radians. So, the answers are:\[g'(x) = -\sin(x)\]and\[g'(1) = -\sin(1)\]The boxes in the original image are provided for students to write their answers.

Name: ### Problem StatementGiven the function \( g(x) = \cos(x) \), find th
Uploaded: 2024-03-20T06:46:42.000Z
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Description: ### Problem StatementGiven the function \( g(x) = \cos(x) \), find the following:1. The derivative of the function \( g'(x) \): \[ g'(x) = \, \underline{\quad \quad} \]2. The value of the derivative at \( x = 1 \): \[ g'(1) = \, \underl