Help Notes: Find the derivative of the function. Simplify if possible. `y = tan^(-1) x^2`

Saturday, 20 October 2012

$\displaystyle{y}=$
tan^(-1) x^2

To determine the derivative of y, use the formula $\displaystyle{\left({{\tan}}^{{-{1}}}\right.}$
u)' = 1/(1+u^2) * u' $\displaystyle.$

$\displaystyle{y}'=\frac{{1}}{{{1}+{{\left({{x}}^{{2}}\right)}}^{{2}}}}\cdot{\left({{x}}^{{2}}\right)}'=\frac{{1}}{{{1}+{{x}}^{{4}}}}\cdot$
2x

$\displaystyle{y}'=\frac{{{2}{x}}}{{{1}+{{x}}^{{4}}}}$

Hence, the
derivative of $\displaystyle{y}={{\tan}}^{{-{1}}}{{x}}^{{2}}$ is $\displaystyle{y}'=\frac{{{2}{x}}}{{{1}+{{x}}^{{4}}}}$ .

Help Notes