d/dx [sin x]
To find the derivative of sin(x) with respect to x, we can use the chain rule
To find the derivative of sin(x) with respect to x, we can use the chain rule.
The chain rule states that if we have a composition of two functions, f(g(x)), the derivative of this composition is given by the product of the derivative of the outer function, f'(g(x)), and the derivative of the inner function, g'(x).
In this case, f(x) = sin(x) and g(x) = x.
The derivative of the outer function, f'(x), is equal to the derivative of sin(x), which is cos(x).
The derivative of the inner function, g'(x), is equal to 1.
Therefore, using the chain rule, we can find the derivative of sin(x) with respect to x:
d/dx [sin(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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