The Derivative of Sin(x) | How to Find and Compute it Using Differentiation Rules

d/dx sin(x)

To find the derivative of the function f(x) = sin(x), we can use the standard rules of differentiation

To find the derivative of the function f(x) = sin(x), we can use the standard rules of differentiation.

The derivative of sin(x) can be computed as follows:

1. Start with the original function f(x) = sin(x).

2. Apply the chain rule: d/dx [f(g(x))] = f'(g(x)) * g'(x).

In this case, g(x) = x, so we have f(x) = sin(x) and g(x) = x.

3. Take the derivative of the outer function f(x) = sin(x).

The derivative of sin(x) with respect to x is cos(x).

Therefore, f'(x) = cos(x).

4. Take the derivative of the inner function g(x) = x.

The derivative of x with respect to x is simply 1.

Therefore, g'(x) = 1.

5. Applying the chain rule, we have:

d/dx [f(g(x))] = f'(g(x)) * g'(x) = cos(x) * 1 = cos(x).

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

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