d/dx (cos x)
To find the derivative of cos x with respect to x, we can use the chain rule
To find the derivative of cos x with respect to x, we can use the chain rule. The chain rule states that if we have a function g(x) inside another function f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) times g'(x).
In this case, the outer function f(x) is simply cos x. The derivative of cos x is given by:
f'(x) = -sin x
Now, let’s consider the inner function g(x), which is just x. The derivative of x with respect to x is simply 1.
Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function:
d/dx (cos x) = -sin x * 1
Simplifying the expression, we get:
d/dx (cos x) = -sin x
Therefore, the derivative of cos x with respect to x is -sin x.
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