d/dx(sinx)
cosx
The derivative of sin(x) with respect to x can be found using the chain rule of calculus. The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:
dy/dx = (dy/du) * (du/dx)
In this case, let y = sin(x) and u = x, so that we have:
dy/du = cos(u)
du/dx = 1
Thus, applying the chain rule, we get:
d/dx(sin(x)) = (dy/du) * (du/dx) = cos(u) * 1 = cos(x)
Therefore, the derivative of sin(x) with respect to x is cos(x).
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