# taking the derivative of trig functions

• Feb 10th 2010, 11:09 AM
TheMathTham
taking the derivative of trig functions
Ok, so here is the equation:
$\displaystyle g(x) = (\arccos (x^{2}))^{5}$

I know that $\displaystyle \arccos(x) = \frac{-1}{\sqrt{1-x^{2}}}$
We use that for taking the integral of $\displaystyle \arccos(x)$, but to do for the derivative?
• Feb 10th 2010, 11:17 AM
icemanfan
You cannot integrate the inverse cosine. To calculate the derivative, use the chain rule:

$\displaystyle g'(x) = 5(\arccos (x^2))^4 * \frac{d}{dx} (\arccos (x^2))$
• Feb 10th 2010, 12:06 PM
TheMathTham
Quote:

Originally Posted by icemanfan
You cannot integrate the inverse cosine. To calculate the derivative, use the chain rule:

$\displaystyle g'(x) = 5(\arccos (x^2))^4 * \frac{d}{dx} (\arccos (x^2))$

oh. I see. its not integration, it just allows for substitution. cool. thanks for the help! the answer i got to match my worksheet was $\displaystyle -10\frac{x(\arccos(x^{2}))^{4}}{\sqrt{1-x^{4}}}$