Enter a problem...
Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
Step 2.1
Differentiate using the chain rule, which states that is where and .
Step 2.1.1
To apply the Chain Rule, set as .
Step 2.1.2
Differentiate using the Power Rule which states that is where .
Step 2.1.3
Replace all occurrences of with .
Step 2.2
Rewrite as .
Step 3
Step 3.1
Differentiate using the Quotient Rule which states that is where and .
Step 3.2
Differentiate.
Step 3.2.1
Differentiate using the Power Rule which states that is where .
Step 3.2.2
Multiply by .
Step 3.2.3
By the Sum Rule, the derivative of with respect to is .
Step 3.2.4
Differentiate using the Power Rule which states that is where .
Step 3.2.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.2.6
Simplify by adding terms.
Step 3.2.6.1
Add and .
Step 3.2.6.2
Multiply by .
Step 3.2.6.3
Subtract from .
Step 3.2.6.4
Add and .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
Step 5.2.1
Cancel the common factor of .
Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Rewrite the expression.
Step 5.2.2
Cancel the common factor of .
Step 5.2.2.1
Cancel the common factor.
Step 5.2.2.2
Divide by .
Step 5.3
Simplify the right side.
Step 5.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.2
Combine.
Step 5.3.3
Simplify the expression.
Step 5.3.3.1
Multiply by .
Step 5.3.3.2
Move to the left of .
Step 5.3.3.3
Reorder factors in .
Step 6
Replace with .