d/dx [ sin(x) ]
cos(x)
We can find the derivative of sin(x) with respect to x using the chain rule of differentiation. The chain rule states that if f(x) is a composite function of g(x), where f(x) = h(g(x)), then the derivative of f(x) with respect to x is given by:
d/dx[f(x)] = (df/dg) * (dg/dx)
Using this rule, let’s differentiate sin(x) with respect to x:
Let f(x) = sin(x), and g(x) = x. Then f(x) is a composite function of g(x) given by f(g(x)) = sin(x).
Using the chain rule, we have
d/dx[sin(x)] = (df/dg) * (dg/dx) = cos(x) * 1 = cos(x)
Therefore, the derivative of sin(x) with respect to x is cos(x).
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