# Find derivatives for the functions. Assume a, b, c, and k are constants. f(x)=\frac{x^{2}+3x+2}{x+1}

Anish Buchanan 2021-05-08 Answered
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{3}{x}+{2}}}{{{x}+{1}}}}$$

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grbavit
First we simplify
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{3}{x}+{2}}}{{{x}+{1}}}}={\frac{{{\left({x}+{1}\right)}{\left({x}+{2}\right)}}}{{{x}+{1}}}}={x}+{2}$$
Then it's just
$$\displaystyle{f}'{\left({x}\right)}={1}$$