Calculus Examples

Find the derivative.
Tap for more steps...
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
Tap for more steps...
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by to get .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Set the derivative equal to then solve the equation .
Tap for more steps...
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Divide each term by and simplify.
Tap for more steps...
Divide each term in by .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor.
Divide by to get .
Solve the original function at .
Tap for more steps...
Replace the variable with in the expression.
Simplify the result.
Tap for more steps...
Simplify each term.
Tap for more steps...
Apply the product rule to .
Raise to the power of to get .
Raise to the power of to get .
Simplify .
Tap for more steps...
Write as a fraction with denominator .
Multiply and to get .
Multiply by to get .
Move the negative in front of the fraction.
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 .
Tap for more steps...
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
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 .
Tap for more steps...
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Add and to get .
Move the negative in front of the fraction.
The final answer is .
The horizontal tangent lines on function are .
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]