sin(x) derivative
The derivative of sin(x) is represented as d/dx(sin(x)) or f'(x), where f(x) is sin(x)
The derivative of sin(x) is represented as d/dx(sin(x)) or f'(x), where f(x) is sin(x). To find the derivative of sin(x), we can apply the chain rule.
The chain rule states that if we have a composite function g(f(x)), the derivative of this composite function with respect to x is equal to the derivative of the outer function evaluated at the inner function (g'(f(x))), multiplied by the derivative of the inner function with respect to x (f'(x)).
In the case of sin(x), the outer function is sin(u) and the inner function is u(x), where u = x. Therefore, g(u) = sin(u) and f(x) = x.
Applying the chain rule, we get:
d/dx(sin(x)) = cos(x) * d/dx(x)
The derivative of x with respect to x is simply 1:
d/dx(sin(x)) = cos(x) * 1
Therefore, the derivative of sin(x) is equal to cos(x).
In short:
d/dx(sin(x)) = cos(x)
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