f(x)= sin(x) f'(x)=
To find the derivative of the function f(x) = sin(x), we can use the differentiation rules for trigonometric functions
To find the derivative of the function f(x) = sin(x), we can use the differentiation rules for trigonometric functions.
The derivative of the function sin(x) is cos(x), so we have:
f'(x) = cos(x)
This means that the rate at which the function sin(x) is changing with respect to x is given by the function cos(x). In other words, the derivative f'(x) tells us the slope of the tangent line to the graph of sin(x) at any given point.
For example, if we want to find the slope of the tangent line to the graph of sin(x) at x = π/4, we can substitute π/4 into the derivative:
f'(π/4) = cos(π/4) = √2/2
So, at x = π/4, the slope of the tangent line to the graph of sin(x) is √2/2.
Note that the derivative of sin(x) is periodic, with a period of 2π. This means that the derivative values repeat after every interval of 2π. Additionally, the derivative of sin(x) is always bounded between -1 and 1, which makes sense because the derivative represents the rate of change and the maximum value for the rate of change of sin(x) is 1.
Overall, the derivative of sin(x) is cos(x), which gives us the rate of change or slope of the tangent line to the graph of sin(x) at any given point.
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