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Chapter 8: Problem 2

Find the derivative of the function. $$ y=5+\sin x $$

Short Answer

Expert verified
The derivative of the function \(y = 5 + \sin x\) is \(\cos x\).

Step by step solution

01

Identify the components of the function

The function that we want to differentiate is \(y = 5 + \sin x\). We see that it has two components: the constant 5, and the sine function \(\sin x\). We'll have to differentiate each term separately.
02

Differentiate the constant 5

The derivative of any constant is 0. Therefore, the derivative of 5 is 0.
03

Differentiate \(\sin x\)

The derivative of \(\sin x\) is \(\cos x\).
04

Combine the results

Now, we take the derivatives we've found and combine them to get the derivative of the whole function. The derivative of \(y = 5 + \sin x\) is \(0 + \cos x\), or just \(\cos x\).

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