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Find the derivative of f(x)\, with respect to x\,: f(x)=\left({\frac  {5x}{7x+9}}\right)^{3}\,

This is a generalized power rule, but the inside function is a quotient.

f'(x)\, =3\left({\frac  {5x}{7x+9}}\right)^{2}{\frac  {d\left({\frac  {5x}{7x+9}}\right)}{dx}}\,
=3\left({\frac  {5x}{7x+9}}\right)^{2}{\frac  {(7x+9)(5)-(5x)(7)}{(7x+9)^{2}}}\,
=3\left({\frac  {5x}{7x+9}}\right)^{2}{\frac  {45}{(7x+9)^{2}}}\,
={\frac  {3375x^{2}}{(7x+9)^{4}}}\,

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