Final answer:
The derivative of sin(x) with respect to x is cos(x). The pattern of the derivatives is sin(x), -cos(x), -sin(x), cos(x), and so on.
Step-by-step explanation:
The derivative of sin(x) with respect to x, denoted as d/dx(sin(x)), can be found by recognizing the pattern that occurs when taking the first few derivatives of sin(x).
The first derivative of sin(x) is cos(x). To find the second derivative, we differentiate cos(x) which gives us -sin(x). Differentiating again gives us -cos(x). We can observe that the pattern continues.
Therefore, the nth derivative of sin(x) alternates between sin(x) and -sin(x), depending on whether n is even or odd.