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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 Quotient Rule which states that is where and .
Step 3.2
Differentiate.
Step 3.2.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.3
Add and .
Step 3.2.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
The derivative of with respect to is .
Step 3.4
Differentiate.
Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.4.5
Add and .
Step 3.5
The derivative of with respect to is .
Step 3.6
Multiply.
Step 3.6.1
Multiply by .
Step 3.6.2
Multiply by .
Step 3.7
Simplify.
Step 3.7.1
Apply the distributive property.
Step 3.7.2
Apply the distributive property.
Step 3.7.3
Simplify the numerator.
Step 3.7.3.1
Combine the opposite terms in .
Step 3.7.3.1.1
Subtract from .
Step 3.7.3.1.2
Add and .
Step 3.7.3.2
Simplify each term.
Step 3.7.3.2.1
Multiply by .
Step 3.7.3.2.2
Multiply by .
Step 3.7.3.3
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .