Differentiate cos x
Understand the Problem
The question is asking for the derivative of the cosine function with respect to the variable x. This involves applying basic differentiation rules in calculus.
Answer
$-\sin(x)$
Answer for screen readers
The derivative of $\cos(x)$ is $-\sin(x)$.
Steps to Solve
- Recall the basic differentiation rule for cosine
The derivative of the cosine function is given by a standard differentiation rule in calculus:
$$ \frac{d}{dx} \cos(x) = -\sin(x) $$
- Apply the differentiation rule
Using the rule directly, we differentiate $\cos(x)$ by replacing it with its derivative:
$$ \frac{d}{dx} \cos(x) = -\sin(x) $$
The derivative of $\cos(x)$ is $-\sin(x)$.
More Information
The cosine function is one of the basic trigonometric functions, and its derivative is another trigonometric function, multiplied by -1.
Tips
A common mistake is forgetting the negative sign when differentiating the cosine function.
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