## d/dx[sin(x)]=

### cos(x)

cos(x)

To find the derivative of sin(x), we use the chain rule, which states that the derivative of a composition of functions is the product of their derivatives.

So, let’s start by considering the function sin(x) as a composition of two functions: f(x) = sin(x) and g(x) = x. We can express this as f(g(x)) = sin(x).

Using the chain rule, we can find the derivative of this composition as:

(d/dx) [f(g(x))] = f'(g(x)) * g'(x)

where f'(g(x)) represents the derivative of the outer function, sin(x), and g'(x) represents the derivative of the inner function, x.

Since the derivative of x with respect to x is just 1, we have:

(d/dx) [sin(x)] = cos(x) * 1

Therefore, we can simplify the derivative of sin(x) as:

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

This means that the derivative of sin(x) is equal to cos(x).

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