Understanding the Chain Rule: Finding the Derivative of sin(x)

ddx sinx

To find the derivative of sin(x), we can use the chain rule of differentiation

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

In this case, sin(x) can be seen as the outer function and x as the inner function. The derivative of sin(x) is found by differentiating the outer function (sin(x)) with respect to the inner function (x) and then multiplying it by the derivative of the inner function, which is 1.

So, according to the chain rule, we have:

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

Since the derivative of x with respect to x is 1, we can simplify further:

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

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

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