Answer:
)/(0.5)=4.7775](https://img.qammunity.org/2020/formulas/mathematics/college/rwucr2a24rl9rkso5wa1e7k8haz9o1bllb.png)
)/(0.125)=1.3999](https://img.qammunity.org/2020/formulas/mathematics/college/rnskj7c7xfzwajaar7upduqtg9kqjzq7kt.png)

For h=0.5:



For h=0.125:



Explanation:
The forward finite difference has the next formula:
)/(h) =(f(x+h)-f(x))/(h)](https://img.qammunity.org/2020/formulas/mathematics/college/dk93b6qy9buoxgjpo469imvmkojw7jeoit.png)
With x=0.25 and h=0.5:
x+h=0.75:

then:

)/(h) = (f(x+h)-f(x))/(h)\\\\](https://img.qammunity.org/2020/formulas/mathematics/college/nvx1cowfdpt9wiskintx89xe4ch8j6ru6l.png)
)/(h) = (4.1079-1.7192)/(0.5)=4.7775\\](https://img.qammunity.org/2020/formulas/mathematics/college/16ngg7rt9uokcgltjv9k7opfglxobfl50p.png)
Now with x=0.25 and h=0.125:
x+h=0.375:

then:

)/(h) = (f(x+h)-f(x))/(h)\\\\](https://img.qammunity.org/2020/formulas/mathematics/college/nvx1cowfdpt9wiskintx89xe4ch8j6ru6l.png)
)/(h) = (1.8942-1.7192)/(0.125)=1.3999\\](https://img.qammunity.org/2020/formulas/mathematics/college/xkqqa3gok32j7g6cozx6s94kbtfslvnmtg.png)
We have to find the derivative at x=0.25:


Now the errors:
For h=0.5:

For h=0.125:
