The derivative of 2sin x with respect to x is 2cos x.
To understand this, we need to recall the basic rules of differentiation, particularly the derivative of the sine function. The derivative of sin x is cos x. Because we have a constant multiplier (2) in front of sin x, we apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.
So, we take the derivative of 2sin x as follows:
- Calculate the derivative of sin x, which is cos x.
- Multiply that result by the constant, which is 2.
This gives us:
Derivative of 2sin x = 2 * cos x = 2cos x.
Therefore, whenever you differentiate a function like 2sin x, remember to treat the 2 as a constant that scales the derivative of the sine function.