Derivative of Cos
d/dx cos(x) = -sin(x)
The derivative of the cosine function is given as:
d/dx(cos(x)) = -sin(x)
This means that the rate of change of the cosine function with respect to its input (x) is equal to the negative sine of x.
To understand this, it helps to visualize the graphs of the sine and cosine functions. The sine function oscillates between -1 and 1, while the cosine function oscillates between 1 and -1. The slope of the sine function at any point is equal to the cosine of that same point, while the slope of the cosine function is equal to the negative sine of the same point.
In other words, at any given point on the graph of the cosine function, the slope (or rate of change) of the function is equal to the negative sine of that point.
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