(d/dx) sin(x)
To find the derivative of sin(x) with respect to x, we will use the chain rule of differentiation
To find the derivative of sin(x) with respect to x, we will use the chain rule of differentiation.
The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).
In this case, we can consider the function y = sin(x) as a composite function where the inner function is g(x) = x and the outer function is f(u) = sin(u).
So, let’s apply the chain rule:
dy/dx = f'(g(x)) * g'(x)
f(u) = sin(u), so f'(u) = cos(u)
g(x) = x, so g'(x) = 1
Now, substitute these values back into the chain rule:
dy/dx = cos(g(x)) * g'(x)
dy/dx = cos(x) * 1
Therefore, the derivative of sin(x) with respect to x is cos(x).
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