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Evaluate differentiation of y with respe...

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

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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: \[ \frac{dy}{dx} = 5 - \sin x \] ---

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: \[ y = 5x + \cos x \] ...
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