If the map is defined as $T:V \rightarrow V$ by $T(f)=f'$ where $f$ is infinitely differentiable. I am trying to show that $T$ is a linear transformation. I understand how to show that it is homogenous but I am struggling to show that it is additive. Please help show that it is additive.
2026-04-04 12:37:55.1775306275
Is $T(f)=f'$ where $f$ is infinitely differentiable an additive transformation?
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You should have learned, in Calculus I, that (f+ g)'= f'+ g' and that (cf)'= cf' for any constant, c.