Evaluate differentiation of y with respect to x :
`y=5x+cosx`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = 5x + \cos x \), we will follow these steps:

### Step 1: Write down the function
We start with the given function:
\[ y = 5x + \cos x \]

### Step 2: Differentiate \( y \) with respect to \( x \)
To find \( \frac{dy}{dx} \), we differentiate each term in the function separately:
\[ \frac{dy}{dx} = \frac{d}{dx}(5x) + \frac{d}{dx}(\cos x) \]

### Step 3: Differentiate the first term \( 5x \)
The derivative of \( 5x \) with respect to \( x \) is:
\[ \frac{d}{dx}(5x) = 5 \]

### Step 4: Differentiate the second term \( \cos x \)
The derivative of \( \cos x \) with respect to \( x \) is:
\[ \frac{d}{dx}(\cos x) = -\sin x \]

### Step 5: Combine the results
Now, we combine the results from the differentiation of both terms:
\[ \frac{dy}{dx} = 5 - \sin x \]

### Final Answer
Thus, the differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 5 - \sin x \]

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