Calculus Examples

Find Where dy/dx is Equal to Zero
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Simplify the expression.
Multiply by .
Reorder terms.
Reform the equation by setting the left side equal to the right side.
Simplify.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply and .
Reorder factors in .
Replace with .
Set then solve for in terms of .
Multiply each term by and simplify.
Multiply each term in by .
Simplify the left side of the equation by cancelling the common factors.
Cancel the common factor of .
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Multiply and .
Divide by .
Simplify terms.
Apply the distributive property.
Reorder.
Rewrite using the commutative property of multiplication.
Move to the left of .
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply .
Multiply by .
Multiply by .
Subtract from .
Multiply by .
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
Set equal to and solve for .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The solution is the result of and .
Exclude the solutions that do not make true.
Simplify .
Simplify each term.
Apply the product rule to .
One to any power is one.
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
is approximately which is negative so negate and remove the absolute value
Find the points where .