derivative of sin(x)
The derivative of sin(x) is calculated using the chain rule of differentiation
The derivative of sin(x) is calculated using the chain rule of differentiation. The chain rule states that if we have a function f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).
In the case of sin(x), the derivative is found by letting f(u) = sin(u) and g(x) = x. Thus, we have f(g(x)) = sin(x).
Next, we need to find the derivative of f(u) = sin(u). The derivative of sin(u) with respect to u is denoted as cos(u), or simply cos u.
Finally, we multiply f'(u) * g'(x). Since f(u) = sin(u), f'(u) = cos(u). And since g(x) = x, g'(x) = 1.
Putting it all together, we have:
f'(g(x)) * g'(x) = cos(g(x)) * 1 = cos(x)
Therefore, the derivative of sin(x) is cos(x).
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