What is the derivative of 4cos(x)?
Understand the Problem
The question is asking for the derivative of the function 4cos(x). To solve this, we will apply the differentiation rule for trigonometric functions, specifically the derivative of cosine.
Answer
The derivative of $4 \cos(x)$ is $-4 \sin(x)$.
Answer for screen readers
The derivative of the function $4 \cos(x)$ is $f'(x) = -4 \sin(x)$.
Steps to Solve
- Identify the function to differentiate
We are given the function to differentiate:
$$ f(x) = 4 \cos(x) $$
- Apply the differentiation rule for cosine
The derivative of $\cos(x)$ is $-\sin(x)$. Therefore, using the constant multiple rule, we differentiate the function:
$$ f'(x) = 4 \cdot (-\sin(x)) $$
- Simplify the derivative
Now we simplify to express the final result:
$$ f'(x) = -4 \sin(x) $$
The derivative of the function $4 \cos(x)$ is $f'(x) = -4 \sin(x)$.
More Information
In differentiation, knowing the basic derivatives of trigonometric functions like sine and cosine is essential. The process of applying these rules helps in tackling more complex functions in calculus.
Tips
- Forgetting to include the negative sign from the derivative of cosine is a common mistake. To avoid this, always remember: the derivative of $\cos(x)$ is $-\sin(x)$.
AI-generated content may contain errors. Please verify critical information
