# Calculus Examples

Find Where dy/dx is Equal to Zero
Step 1
Differentiate both sides of the equation.
Step 2
The derivative of with respect to is .
Step 3
Differentiate the right side of the equation.
Step 3.1
Differentiate.
Step 3.1.1
By the Sum Rule, the derivative of with respect to is .
Step 3.1.2
Differentiate using the Power Rule which states that is where .
Step 3.2
Evaluate .
Step 3.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.2
Differentiate using the Power Rule which states that is where .
Step 3.2.3
Multiply by .
Step 3.3
Reorder terms.
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Replace with .
Step 6
Set then solve for in terms of .
Step 6.1
Subtract from both sides of the equation.
Step 6.2
Divide each term in by and simplify.
Step 6.2.1
Divide each term in by .
Step 6.2.2
Simplify the left side.
Step 6.2.2.1
Cancel the common factor of .
Step 6.2.2.1.1
Cancel the common factor.
Step 6.2.2.1.2
Divide by .
Step 6.2.3
Simplify the right side.
Step 6.2.3.1
Move the negative in front of the fraction.
Step 7
Solve for .
Step 7.1
Remove parentheses.
Step 7.2
Remove parentheses.
Step 7.3
Simplify .
Step 7.3.1
Simplify each term.
Step 7.3.1.1
Use the power rule to distribute the exponent.
Step 7.3.1.1.1
Apply the product rule to .
Step 7.3.1.1.2
Apply the product rule to .
Step 7.3.1.2
Raise to the power of .
Step 7.3.1.3
Multiply by .
Step 7.3.1.4
One to any power is one.
Step 7.3.1.5
Raise to the power of .
Step 7.3.1.6
Cancel the common factor of .
Step 7.3.1.6.1
Factor out of .
Step 7.3.1.6.2
Cancel the common factor.
Step 7.3.1.6.3
Rewrite the expression.
Step 7.3.2
To write as a fraction with a common denominator, multiply by .
Step 7.3.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 7.3.3.1
Multiply by .
Step 7.3.3.2
Multiply by .
Step 7.3.4
Combine the numerators over the common denominator.
Step 7.3.5