Calculus Examples

Differentiate both sides of the equation.
Differentiate the left side of the equation.
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...
Differentiate using the chain rule, which states that is where and .
Tap for more steps...
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Differentiate the right side of the equation.
Tap for more steps...
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by to get .
Simplify.
Tap for more steps...
Apply the distributive property.
Remove parentheses around .
Reform the equation by setting the left side equal to the right side.
Solve for .
Tap for more steps...
Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
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 .
Simplify the right side of the equation.
Tap for more steps...
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Factor out of .
Multiply by to get .
Simplify with factoring out.
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
Tap for more steps...
Rewrite as .
Move the negative in front of the fraction.
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 .
Simplify the right side of the equation.
Tap for more steps...
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Tap for more steps...
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Multiply and to get .
Replace with .
Enter YOUR Problem
Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]