derv cos(x)
To find the derivative of cos(x), we can use the chain rule
To find the derivative of cos(x), we can use the chain rule. The chain rule states that if u = f(x) and y = g(u), then the derivative of y with respect to x is given by dy/dx = (dy/du) * (du/dx).
In this case, u = x and y = cos(u). So, we need to find (dy/du) and (du/dx).
The derivative of cos(u) with respect to u is given by (dy/du) = -sin(u). Notice that we replace x with u in this case.
The derivative of u = x with respect to x is simply (du/dx) = 1.
Finally, applying the chain rule, we have:
dy/dx = (dy/du) * (du/dx)
= -sin(u) * 1
= -sin(x)
Therefore, the derivative of cos(x) is -sin(x).
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