Math Help Forum - View Single Post - Pre-Cal: Deriviatives & Graph Line Tangent

Aryth · #2 November 25th, 2008, 01:06 AM

1) $f(x) = \left(\frac{(x^2 -1)}{\sqrt{x}}\right)^4$

1: Distribute the power of 4.

$f(x) = \left(\frac{(x^2 - 1)^4}{\sqrt{x}^4}\right)$

2: Simplify the denominator:

$f(x) = \left(\frac{(x^2 - 1)^4}{x^2}\right)$

3: Use the following rule:

$\frac{d}{dx}\left[\frac{u}{v}\right] = \frac{u'v - vu'}{v^2}$

4: Solve:

$f'(x) = \frac{8x(x^2 - 1)^3*x^2 - (x^2 - 1)^4*2x}{x^4}$

5. Simplify:

$f'(x) = 2x(x^2 - 1)^3\frac{4x^2 - (x^2 - 1)}{x^4}$

$f'(x) = 2x(x^2 - 1)^3\frac{3x^2 + 1}{x^4}$

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