What is the derivative of cos y?
Understand the Problem
The question is asking for the derivative of the cosine function with respect to y. This is a straightforward calculus problem, and the derivative of cos(y) is -sin(y).
Answer
The derivative of $\cos(y)$ is $-\sin(y)$.
Answer for screen readers
The derivative of $\cos(y)$ with respect to $y$ is $-\sin(y)$.
Steps to Solve
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Identify the function
The function given is $f(y) = \cos(y)$. -
Apply the derivative rule
To find the derivative of the cosine function, we use the known derivative rule: if $f(y) = \cos(y)$, then $f'(y) = -\sin(y)$. -
Write the final answer
Thus, the derivative of $\cos(y)$ with respect to $y$ is:
$$ f'(y) = -\sin(y) $$
The derivative of $\cos(y)$ with respect to $y$ is $-\sin(y)$.
More Information
The derivative of the cosine function is one of the fundamental derivatives in calculus. It is useful in various applications, including physics, engineering, and any time you are working with oscillatory phenomena.
Tips
- A common mistake is to confuse the derivatives of the sine and cosine functions. Remember that the derivative of $\sin(y)$ is $\cos(y)$, while the derivative of $\cos(y)$ is $-\sin(y)$.
