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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Step 3.1
Differentiate using the Product Rule which states that is where and .
Step 3.2
Differentiate using the chain rule, which states that is where and .
Step 3.2.1
To apply the Chain Rule, set as .
Step 3.2.2
The derivative of with respect to is .
Step 3.2.3
Replace all occurrences of with .
Step 3.3
Combine and .
Step 3.4
The derivative of with respect to is .
Step 3.5
Multiply by .
Step 3.6
Multiply by by adding the exponents.
Step 3.6.1
Multiply by .
Step 3.6.1.1
Raise to the power of .
Step 3.6.1.2
Use the power rule to combine exponents.
Step 3.6.2
Add and .
Step 3.7
To multiply absolute values, multiply the terms inside each absolute value.
Step 3.8
Raise to the power of .
Step 3.9
Raise to the power of .
Step 3.10
Use the power rule to combine exponents.
Step 3.11
Add and .
Step 3.12
Differentiate using the Power Rule which states that is where .
Step 3.13
Simplify.
Step 3.13.1
Reorder terms.
Step 3.13.2
Simplify each term.
Step 3.13.2.1
Remove non-negative terms from the absolute value.
Step 3.13.2.2
Cancel the common factor of and .
Step 3.13.2.2.1
Factor out of .
Step 3.13.2.2.2
Cancel the common factors.
Step 3.13.2.2.2.1
Multiply by .
Step 3.13.2.2.2.2
Cancel the common factor.
Step 3.13.2.2.2.3
Rewrite the expression.
Step 3.13.2.2.2.4
Divide by .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .