Tính $\frac{f\text{'}\left(1\right)}{\phi \text{'}\left(1\right)}$ biết rằng f(x)=$4x+\sin \frac{\mathrm{\pi x}}{2}$.

Giải

$$\begin{gathered} Ta có f\text{'}\left(1\right)=2x\Rightarrow f\text{'}\left(1\right)=2; \phi \text{'}\left(x\right)=4+\frac{\mathrm{\pi }}{2}\cos \frac{\mathrm{\pi x}}{2}\Rightarrow \phi \text{'}\left(1\right)=4 \\ Vậy \frac{f\text{'}\left(1\right)}{\phi \text{'}\left(1\right)}=\frac{2}{4}=\frac{1}{2} \end{gathered}$$