d/dx [cos x]
To find the derivative of cosine of x, denoted as d/dx [cos x], we can use the chain rule
To find the derivative of cosine of x, denoted as d/dx [cos x], we can use the chain rule.
The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative of this composition is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
In this case, we have the function f(x) = cos x. The derivative of cosine function is equal to the negative sine function, which we can denote as -sin x. Therefore, f'(x) = -sin x.
Now, applying the chain rule, we can write:
d/dx [cos x] = d/dx [f(g(x))]
Where f(x) = cos x and g(x) = x.
Using the chain rule, we have:
d/dx [f(g(x))] = f'(g(x)) * g'(x)
Substituting our function and its derivative:
d/dx [cos x] = (-sin x) * 1
Simplifying, we get:
d/dx [cos x] = -sin x
Therefore, the derivative of the cosine of x, d/dx [cos x], is equal to negative sine of x, -sin x.
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