{"id":237517,"date":"2024-04-13T16:14:23","date_gmt":"2024-04-13T16:14:23","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=237517"},"modified":"2024-04-13T16:14:23","modified_gmt":"2024-04-13T16:14:23","slug":"how-to-differentiate-absolute-value-functions","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-differentiate-absolute-value-functions\/","title":{"rendered":"How to differentiate absolute value functions?"},"content":{"rendered":"

To differentiate absolute value functions, you need to remember that the absolute value function |x| can be defined piecewise as follows: |x| = x if x \u2265 0 and |x| = -x if x < 0. To differentiate, determine whether the input value x is positive or negative, and then apply the appropriate rule.\n\n\n**When x \u2265 0:**\n\n\nd\/dx(|x|) = d\/dx(x) = 1\n\n\n**When x < 0:**\n\n\nd\/dx(|x|) = d\/dx(-x) = -1\n\n\nSo, the derivative of the absolute value function |x| is:\n\n\nd\/dx(|x|) = 1 if x > 0 and d\/dx(|x|) = -1 if x < 0\n\n\nTherefore, the techniques to differentiate the absolute value function involves considering the sign of the input value x and using the piecewise definition to find the derivative accordingly.\n\n\n\n\n

\n
\n

Table of Contents<\/p>\nToggle<\/span><\/path><\/svg><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n