Calculus Examples

Find the Derivative - d/dx 2-|2x-1|
Step 1
Differentiate.
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Step 1.1
By the Sum Rule, the derivative of with respect to is .
Step 1.2
Since is constant with respect to , the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the chain rule, which states that is where and .
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Step 2.2.1
To apply the Chain Rule, set as .
Step 2.2.2
The derivative of with respect to is .
Step 2.2.3
Replace all occurrences of with .
Step 2.3
By the Sum Rule, the derivative of with respect to is .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Differentiate using the Power Rule which states that is where .
Step 2.6
Since is constant with respect to , the derivative of with respect to is .
Step 2.7
Multiply by .
Step 2.8
Add and .
Step 2.9
Combine and .
Step 2.10
Move to the left of .
Step 3
Simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Combine terms.
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Step 3.2.1
Multiply by .
Step 3.2.2
Multiply by .
Step 3.2.3
Subtract from .
Step 3.3
Factor out of .
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Step 3.3.1
Factor out of .
Step 3.3.2
Factor out of .
Step 3.3.3
Factor out of .