Question

Derivative of x(t) = 3 - |t - 3| ?

i don't know how to find the derivative of an absolute value... help plz

Answer 1

Derivative of absolute value is simple..

|x| =
x, x > 0
-x, x < 0

Differentiation gives:
d/dx |x| =
1, x > 0
-1, x < 0

Answer 2

Use the chain rule on the rest of it.

Answer 3

The function I provided actually is sometimes written as sign(x)
It can also be written as x/|x|

Answer 4

So you could use
d/dx |x| = x / |x|

Answer 5

Simple way is to rewrite the function without the absolute value for t>3 and then for t<3.

Answer 6

if memory serves:\[\frac d{dx}|f(x)|\to\frac{f(x)}{|f(x)|}f'(x)\]
\[|c-x|'\to\frac{c-x}{|c-x|}~(-1)\]

Answer 7

@wio Thanks!