Campos Garza
02/16/2024 · Primary School
If \( g(x)=\cos (x) \) then \( g^{\prime}(x)=\square \) \( g^{\prime}(1)=\square \)
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Step-by-step Solution
To find the derivative of the function \( g(x) = \cos(x) \), we can use the standard derivative rule for cosine.
1. The derivative of \( g(x) = \cos(x) \) is:
\[
g'(x) = -\sin(x)
\]
2. Now, we need to evaluate \( g'(1) \):
\[
g'(1) = -\sin(1)
\]
Thus, we can fill in the squares:
- \( g^{\prime}(x) = -\sin(x) \)
- \( g^{\prime}(1) = -\sin(1) \)
Quick Answer
\( g^{\prime}(x) = -\sin(x) \)
\( g^{\prime}(1) = -\sin(1) \)
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