Given the function:

$y = \sin(x)$

To find the first derivative, $y'$, and the second derivative, $y''$, we proceed as follows:

Step 1: Find the first derivative ($y'$)

The derivative of $\sin(x)$ with respect to $x$ is:

$y' = \cos(x)$

Step 2: Find the second derivative ($y''$)

Now, take the derivative of $y' = \cos(x)$. The derivative of $\cos(x)$ is:

$y'' = -\sin(x)$

Final Answer:

$y' = \cos(x)$ $y'' = -\sin(x)$

Would you like further clarification or details on these steps?

Here are 5 related questions for further practice:

1. What is the third derivative of $y = \sin(x)$?
2. What is the derivative of $y = \cos(x)$?
3. How would you differentiate $y = \sin(2x)$?
4. What is the second derivative of $y = \sin^2(x)$?
5. How do you find the derivative of $y = e^x \sin(x)$?

Tip: To find the second derivative of a function, simply differentiate the first derivative again.