Chain Rule

Find the derivative, \( f'(x) \) of the following functions.

1. \(\displaystyle{f(x)= (2x-5)^4} \)    solution      

2. \(\displaystyle{f(x)= (1- x^2)^7} \)     solution 

3. \(\displaystyle{f(x)= \sqrt{x^2-5x+1}}\)    solution

4. \(\displaystyle{f(x)= \sqrt[3]{x^2-x+2}} \)    solution

5. \(\displaystyle{f(x)= \frac{1}{(3x-1)^4}} \)    solution

6. \(\displaystyle{f(x)=\frac{3}{\sqrt{4x^2+3}}} \)      solution

7. \(\displaystyle{f(x)= (x^2+1)^3(5x+1)^2} \)   solution

8. \(\displaystyle{f(x)=\frac{1-x^2}{\sqrt{2x+7}}} \)   solution

9. \(\displaystyle{f(x)=\left( x - \frac{1}{x}\right)^2} \)   solution