๐/๐๐ฅ[cos ๐ฅ]
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 we have the composition of two functions f(g(x)), then the derivative is given by f'(g(x)) * g'(x).
In this case, we have the function f(x) = cos(x), and g(x) = x. So, applying the chain rule, we have:
๐/๐๐ฅ[cos ๐ฅ] = f'(g(x)) * g'(x).
The derivative of f(x) = cos(x) is simply the negative sine function, so f'(x) = -sin(x).
The derivative of g(x) = x is 1 since the derivative of x with respect to x is always 1.
Now, substituting these values into the chain rule formula, we get:
๐/๐๐ฅ[cos ๐ฅ] = -sin(x) * 1 = -sin(x).
Therefore, the derivative of cos(x) with respect to x is -sin(x).
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