d/dx cos x
The notation “d/dx” represents the process of differentiating a function with respect to the variable x
The notation “d/dx” represents the process of differentiating a function with respect to the variable x. In this case, we want to find the derivative of the cosine function, which is denoted as “cos x”.
To differentiate cos x, we can use the chain rule. The chain rule allows us to differentiate composite functions. In this case, the function is a composition of the cosine function with the identity function (f(x) = x).
Applying the chain rule, we start by differentiating the outer function (cos x) with respect to its inside function (x), and then multiply it by the derivative of the inside function (which is 1 in this case).
So, using the chain rule, we have:
d/dx (cos x) = (d/dx) (cos x) * (d/dx) (x)
The derivative of the cosine function (d/dx) (cos x) is obtained by differentiating its standard form, which is -sin x. Hence:
d/dx (cos x) = -sin x * (d/dx) (x)
Since the derivative of the identity function (d/dx) (x) is 1, the expression simplifies to:
d/dx (cos x) = -sin x
Therefore, the derivative of the cosine function cos x with respect to x is simply -sin x.
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