d/dx[sin(x)]
The derivative of the sine function, denoted as d/dx[sin(x)], represents how the value of sine changes with respect to the independent variable x
The derivative of the sine function, denoted as d/dx[sin(x)], represents how the value of sine changes with respect to the independent variable x. To find this derivative, we can use the rules of differentiation and apply them to the sine function.
The derivative of sine is found by differentiating it as if it were a composite function. Recall that the derivative of a composite function can be calculated using the chain rule:
If we have a composite function f(g(x)), the derivative of f(g(x)) with respect to x is given by d/dx[f(g(x))] = f'(g(x)) * g'(x).
In our case, f(x) is the sine function, and x is our variable. Therefore, g(x) = x.
Now, let’s differentiate the sine function with respect to x:
d/dx[sin(x)] = cos(x)
So, the derivative of the sine function with respect to x is simply the cosine of x, written as cos(x).
This means that at any particular point on the sine curve, the rate of change of the function is given by the cosine function.
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