# Calculus Examples

Step 1
Differentiate both sides of the equation.
Step 2
Differentiate the left side of the equation.
Step 2.1
Differentiate.
Step 2.1.1
By the Sum Rule, the derivative of with respect to is .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.2
Evaluate .
Step 2.2.1
Differentiate using the chain rule, which states that is where and .
Step 2.2.1.1
To apply the Chain Rule, set as .
Step 2.2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.2.1.3
Replace all occurrences of with .
Step 2.2.2
Rewrite as .
Step 3
Since is constant with respect to , the derivative of with respect to is .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Solve for .
Step 5.1
Subtract from both sides of the equation.
Step 5.2
Divide each term in by and simplify.
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Step 5.2.2.1
Cancel the common factor of .
Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Rewrite the expression.
Step 5.2.2.2
Cancel the common factor of .
Step 5.2.2.2.1
Cancel the common factor.
Step 5.2.2.2.2
Divide by .
Step 5.2.3
Simplify the right side.
Step 5.2.3.1
Cancel the common factor of and .
Step 5.2.3.1.1
Factor out of .
Step 5.2.3.1.2
Cancel the common factors.
Step 5.2.3.1.2.1
Factor out of .
Step 5.2.3.1.2.2
Cancel the common factor.
Step 5.2.3.1.2.3
Rewrite the expression.
Step 5.2.3.2
Move the negative in front of the fraction.
Step 6
Replace with .