Mastering the Chain Rule: The Derivative of f(x) = cos(x) with Respect to x Revealed

d/dx cosx

To find the derivative of the function f(x) = cos(x) with respect to x, we can use the derivative rules

To find the derivative of the function f(x) = cos(x) with respect to x, we can use the derivative rules. In this case, we will use the chain rule.

The chain rule states that if we have a composite function, f(g(x)), then the derivative of that function 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, our composite function is f(x) = cos(x). We can think of cos(x) as the outer function and x as the inner function.

The derivative of the outer function cos(x) can be found by using the derivative of the trigonometric function rule. The derivative of cos(x) is equal to -sin(x).

The derivative of the inner function, x, with respect to x is 1.

Applying the chain rule, we have:

d/dx cos(x) = (-sin(x)) * (1) = -sin(x).

Therefore, the derivative of f(x) = cos(x) with respect to x is -sin(x).

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