Solve for dy/dx where y = f(x) = |x|?

Question

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Answer 1

the given function is not differentiable at x=0

therefore, f(x) = x for x>0 dy/dx = 1
f(x) = -x for x<0 dy/dx = -1

Answer 2

1

Answer 3

When you derive the absolute value of a function, say derivative of |f(x)|, the derivative is always equal to f(x)/|f(x)| * d(f(x)). In this case, the f(x) would be simply x, so the derivative would be x/|x|*1. This statement is equal to 1 for all values for which x>0, though, and -1 for all values which x<0 (you can plug in to find that out). At x=0, though, you can see that the derivative is not defined (0/0).

Answer 4

Since y is the absolute value of x, it cant take any negative values.
Hence y=+x.

Hence d(y)/dx = d(x)/dx= 1.

Answer 5

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Answer 6

Magic above is correct.

Note the function is not differentiable only at the point x = 0

Answer 7

it is 1 for x>0 and -1 for x<0
*Break it down to a hybird function

Answer 8

the dy/dx does not exsist as in |x| x has two values +or- and in differentiation there is only one value possilble

Answer 9

lxl/x=1forxnot equal to 0 and x>0
it is not differentiable at x=0

Answer 10

absolute x means thevalue is either -x or x thererfore on diferentiation, the answer will be 1 or -1.