The Chain Rule | Finding the Derivative of the Cosine Function

d/dx (cos x) =

To find the derivative of cosine function, we can use the rules of differentiation

To find the derivative of cosine function, we can use the rules of differentiation.

The derivative of cosine function can be found using the chain rule. The chain rule states that if we have a composite function, where one function is nested inside another, then the derivative of the composite function can be found by multiplying the derivative of the outer function with the derivative of the inner function.

In this case, we have the cosine function, which can be written as f(x) = cos(x). To find its derivative with respect to x, we differentiate each part separately.

The derivative of the outer function, which is cosine, can be found using the derivative formula for cosine, which is -sin(x).

The derivative of the inner function, which is x, is simply 1.

Now, applying the chain rule, we multiply the derivative of the outer function with the derivative of the inner function:

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

So, the derivative of the cosine function with respect to x is -sin(x).

In summary:

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

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