Final answer:
The derivative of the function h(t) = 2sin(t) is h'(t) = 2cos(t), found by applying the basic differentiation rule for the sine function and preserving the constant.
Step-by-step explanation:
The derivative of the function h(t) = 2sin(t) is h'(t) = 2cos(t).To find the derivative of h(t), we apply the basic differentiation rule for sine, which states that the derivative of sin(t) with respect to t is cos(t). Since we have a constant multiple (2) in front of sin(t), according to the constant multiple rule, this constant is preserved when taking the derivative.
Therefore, the final derivative of the function h(t) = 2sin(t) is simply 2 times the derivative of sin(t), which is 2cos(t). We do not need additional trigonometric identities or complex calculations for this problem, as it is a straightforward application of differentiation rules for trigonometric functions.h'(t) = 2cos(tThe derivative of a sine function is a cosine function. To differentiate 2sin(t), we use the power rule and take the derivative of the coefficient, which is 2, and multiply it by the derivative of the sine function, which is cos(t). Therefore, h'(t) = 2cos(t).