If f(x) is an antiderivative of g(x), and g(x) is an antiderivative of h(x), then the correct expression is:
Option A; f"(x)=h(x)
We are told that;
f(x) is an antiderivative of g(x)
Thus;
f'(x) = g(x) ---(eq 1)
We are told that;
g(x) is an antiderivative of h(x)
Thus; g'(x) = h(x) ----(eq 2)
From eq 1, let us find the second derivative of f(x) to get;
f''(x) = g'(x)
Let us put f''(x) for g'(x) in eq 2 to get;
f''(x) = h(x)
In conclusion, the correct statement is f''(x) = h(x)
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