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Problem 2-9: Differentiating Polynomial and Rational Functions


Differentiate
a)  f\left(x\right)= 1+ 2x
b)  f\left(x\right)= 1 - 2x + 2x^2
c)  f\left(x\right)= 1- x^2 +\frac{1}{x}
d)  f\left(x\right)= 1 - x +\frac{1}{1-x}


Solution
The following rules can be used:
I)  \displaystyle\frac{d}{dx}ax^n=anx^{n-1}
II)  \displaystyle\frac{d}{dx}\left(u+v\right)=\frac{du}{dx}+\frac{dv}{dx}
III)  \displaystyle\frac{d}{dx}\frac{u}{v}=\frac{1}{v^2}\left(v\frac{du}{dx}-u\frac{dv}{dx}\right)
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