(d/dx) cos(x)
The expression (d/dx) cos(x) represents the derivative of the cosine function with respect to x
The expression (d/dx) cos(x) represents the derivative of the cosine function with respect to x. To calculate this derivative, we will use the chain rule.
The chain rule states that if we have a function of the form f(g(x)), where f(x) and g(x) are both differentiable functions, then the derivative of f(g(x)) with respect to x is given by:
(f(g(x)))’ = f'(g(x)) * g'(x)
In this case, f(x) is cos(x) and g(x) is x.
The derivative of cos(x) is given by -sin(x) (using the derivative of a cosine function as a trigonometric identity).
The derivative of x with respect to x is simply 1.
Using the chain rule, we can calculate the derivative of cos(x) with respect to x:
(d/dx) cos(x) = -sin(x) * 1 = -sin(x)
Therefore, (d/dx) cos(x) = -sin(x).
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