The Chain Rule: Finding the Derivative of sin(x) with Respect to x and the Surprising Result

d/dx sin(x)

To find the derivative of sin(x) with respect to x, we can use the chain rule

To find the derivative of sin(x) with respect to x, we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative of the composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is sin(x) and there is no inner function, so the derivative of sin(x) is simply the derivative of the outer function.

The derivative of cosine is negative sine, so:

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

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

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