how do i differentiate abs(x^2-1)? please help me

Question

dumbcow · Answer

you have to split it up because it cannot be differentiated at points x= +-1

mrdoe · Answer

rewrite as $$\sqrt{(x ^{2}-1}^{2}$$

anonymous · Answer

work in cases

mrdoe · Answer

except with correct placement on that parentheses

anonymous · Answer

if $x<-1$ or $x>1$ it is $x^2-1$ but if $-1<x<1$ it is $1-x^2$

anonymous · Answer

both of those are very easy to differentiate
your derivative is a piecewise function

anonymous · Answer

which is not surprising since so is $f(x)=|x^2-1|$

anonymous · Answer

so I should differentiate x^2-1 and 1-2x^2?

anonymous · Answer

yes,

anonymous · Answer

well no not $1-2x^2$just $1-x^2$

anonymous · Answer

so 2x and -2x are the answers?

anonymous · Answer

yes

anonymous · Answer

depending on the values of $x$ it is piecewise

anonymous · Answer

you are awesome bro can i adopt you?

anonymous · Answer

$$f'(x) = \left\{\begin{array}{rcc}
2x& \text{if}  & x< -1 \text{ or} x>1\
-2x& \text{if}  &-1< x < 1
\end{array}
\right.
$$

anonymous · Answer

which is exactly because 
$$f(x) = |x^2-1| = \left\{\begin{array}{rcc}
x^2-1 & \text{if}  & x<-1 \text { or } x>1 \
1-x^2& \text{if}  & -1<x < 1
\end{array}
\right.
$$

anonymous · Answer

thanks you can buy me a whiskey at the bar

anonymous · Answer

thank you.I'll send you that whiskey asap :D