Calc2.35

From Example Problems
Revision as of 18:34, 2 March 2006 by Geoff (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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}}}\,




Main Page : Calculus