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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
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Quotient Rule which states that is where and .
Step 3.3
Differentiate.
Step 3.3.1
Differentiate using the Power Rule which states that is where .
Step 3.3.2
Multiply by .
Step 3.3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.5
Add and .
Step 3.3.6
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.7
Multiply.
Step 3.3.7.1
Multiply by .
Step 3.3.7.2
Multiply by .
Step 3.4
The derivative of with respect to is .
Step 3.5
Combine and .
Step 3.6
Simplify.
Step 3.6.1
Apply the distributive property.
Step 3.6.2
Simplify each term.
Step 3.6.2.1
Multiply by .
Step 3.6.2.2
Multiply by .
Step 3.6.3
Reorder terms.
Step 3.6.4
Factor out of .
Step 3.6.4.1
Factor out of .
Step 3.6.4.2
Factor out of .
Step 3.6.4.3
Factor out of .
Step 3.6.4.4
Factor out of .
Step 3.6.4.5
Factor out of .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .