- #1
nil1996
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how do we take derivative of modulus of a function??
Derivative of modulus of a function
- Thread starter nil1996
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In summary, the derivative of modulus of a function is the slope of the tangent line to the absolute value of the function at a specific point, and it is calculated using the limit definition of the derivative. It is undefined at non-differentiable points and is always positive or zero. The derivative has practical applications in various fields, such as determining maximum/minimum values and calculating rates of change. It cannot be negative, as the absolute value of a number is always positive or zero.
- #2
tiny-tim
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hi nil1996! 
|f(x)| = f(x) times sign(f(x))
so you can use the product rule, except where f(x) = 0 (where |f|' won't exist unless f' = 0)
|f(x)| = f(x) times sign(f(x))
so you can use the product rule, except where f(x) = 0 (where |f|' won't exist unless f' = 0)
- #3
brmath
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Are you talking about a function of a real or complex variable?
FAQ: Derivative of modulus of a function
What is the definition of the derivative of modulus of a function?
The derivative of modulus of a function is a mathematical concept used to describe the rate of change of a function at a specific point. It is defined as the slope of the tangent line to the graph of the absolute value of the function at that point.
How is the derivative of modulus of a function calculated?
The derivative of modulus of a function is calculated using the limit definition of the derivative. This involves finding the limit as the change in x approaches 0 of the difference quotient, which is the change in y divided by the change in x. The result of this limit is the slope of the tangent line at the given point.
What are some properties of the derivative of modulus of a function?
Some properties of the derivative of modulus of a function include:
- The derivative is undefined at points where the function is not differentiable.
- The derivative is always positive or zero, since the absolute value of a number cannot be negative.
- The derivative exists at all points where the function is differentiable.
How is the derivative of modulus of a function used in real-world applications?
The derivative of modulus of a function has many practical applications, such as in physics, economics, and engineering. For example, it can be used to determine the maximum or minimum value of a function, which is useful in optimization problems. It can also be used to calculate rates of change, such as velocity or acceleration, in various systems.
Can the derivative of modulus of a function be negative?
No, the derivative of modulus of a function cannot be negative. This is because the absolute value of a number is always positive or zero, and the derivative measures the rate of change of the absolute value of the function. Therefore, the derivative can only be positive or zero at any given point.