Question

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

Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{a}^{{{2}}}-{x}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}$$

$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{a}^{{{2}}}-{x}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}=-{\frac{{-{a}^{{{2}}}+{x}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}=-{\frac{{{a}^{{{2}}}+{x}^{{{2}}}-{2}{a}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}=-{1}+{2}{\frac{{{a}^{{{2}}}}}{{{a}^{{{2}}}+{x}^{{{2}}}}}}$$
$$\displaystyle{\left({\frac{{{1}}}{{{g{{\left({x}\right)}}}'}}}=-{\frac{{{g}'{\left({x}\right)}}}{{{\left[{g{{\left({x}\right)}}}\right]}^{{{2}}}}}}\right.}$$
$$\displaystyle{f}'{\left({x}\right)}=-{2}{a}^{{{2}}}{\frac{{{\left({a}^{{{2}}}+{x}^{{{2}}}\right)}'}}{{{\left({a}^{{{2}}}+{x}^{{{2}}}\right)}^{{{2}}}}}}-{\frac{{{4}{a}^{{{a}}}{x}}}{{{\left({a}^{{{2}}}+{x}^{{{2}}}\right)}^{{{2}}}}}}$$