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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