Question

If \[\frac{d}{dx}[F(x)]=\frac{d}{dx}[G(x)],\] what follows?

Options

• \[F(x)=G(x)+C\]

• \[F(x)=G'(x)+C\]

• \[F(x)=G(x)\]

• \[F'(x)=G(x)+C\]

Answer 1

When \[F(x)\] and \[G(x)\] have the same derivative, their difference has derivative zero. Thus, their difference is a constant, giving \[F(x)=G(x)+C.\]