d/dx(sinx)
cosx
The derivative of sin(x) with respect to x is cosine(x).
We can prove this using the chain rule. The derivative of sin(x) can be written as:
dy/dx = dy/du * du/dx
where y = sin(x) and u = x.
Now, the derivative of y = sin(u) with respect to u is:
dy/du = cos(u)
and the derivative of u = x with respect to x is:
du/dx = 1
Therefore, the full derivative of sin(x) is:
dy/dx = dy/du * du/dx = cos(u) * 1 = cos(x)
So, the derivative of sin(x) with respect to x is cos(x).
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