derivative of 2sinx
Understand the Problem
The question is asking for the derivative of the function 2sin(x). This requires the application of basic differentiation rules in calculus.
Answer
2cos(x)
Answer for screen readers
The final answer is 2cos(x)
Steps to Solve
- Understanding differentiation rules for trigonometric functions
To find the derivative of a trigonometric function, we use standard differentiation rules. Specifically, the derivative of $\sin(x)$ is $\cos(x)$.
- Applying the constant multiple rule
If we have a function multiplied by a constant, like $2\sin(x)$, the constant can be pulled out, and the differentiation applies only to the trigonometric part. So, we write $\frac{d}{dx}[2\sin(x)] = 2 \cdot \frac{d}{dx}[\sin(x)]$.
- Finding the derivative of the trigonometric part
We know $\frac{d}{dx}[\sin(x)] = \cos(x)$. Substituting this, we get $2 \cdot \cos(x)$.
- Combining the results
Putting it all together, the derivative of $2\sin(x)$ is $2\cos(x)$. Thus, $\frac{d}{dx}[2\sin(x)] = 2\cos(x)$.
The final answer is 2cos(x)
More Information
The derivative 2cos(x) represents the rate of change of the function 2sin(x) with respect to x.
Tips
A common mistake is to forget to multiply the differentiation result by the constant outside the function. Always consider the constant multiple rule when differentiating functions with constant coefficients.
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