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Calculus Examples
Step 1
Differentiate both sides of the equation.
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Evaluate .
Step 2.2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2.2
Differentiate using the Power Rule which states that is where .
Step 2.2.3
Combine and .
Step 2.2.4
Combine and .
Step 2.2.5
Cancel the common factor of and .
Step 2.2.5.1
Factor out of .
Step 2.2.5.2
Cancel the common factors.
Step 2.2.5.2.1
Factor out of .
Step 2.2.5.2.2
Cancel the common factor.
Step 2.2.5.2.3
Rewrite the expression.
Step 2.3
Evaluate .
Step 2.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.3.2
Differentiate using the chain rule, which states that is where and .
Step 2.3.2.1
To apply the Chain Rule, set as .
Step 2.3.2.2
Differentiate using the Power Rule which states that is where .
Step 2.3.2.3
Replace all occurrences of with .
Step 2.3.3
Rewrite as .
Step 2.3.4
Combine and .
Step 2.3.5
Combine and .
Step 2.3.6
Combine and .
Step 2.3.7
Move to the left of .
Step 2.3.8
Cancel the common factor of and .
Step 2.3.8.1
Factor out of .
Step 2.3.8.2
Cancel the common factors.
Step 2.3.8.2.1
Factor out of .
Step 2.3.8.2.2
Cancel the common factor.
Step 2.3.8.2.3
Rewrite the expression.
Step 3
Since is constant with respect to , the derivative of with respect to is .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Step 5.1
Subtract from both sides of the equation.
Step 5.2
Multiply both sides of the equation by .
Step 5.3
Simplify both sides of the equation.
Step 5.3.1
Simplify the left side.
Step 5.3.1.1
Cancel the common factor of .
Step 5.3.1.1.1
Cancel the common factor.
Step 5.3.1.1.2
Rewrite the expression.
Step 5.3.2
Simplify the right side.
Step 5.3.2.1
Simplify .
Step 5.3.2.1.1
Cancel the common factor of .
Step 5.3.2.1.1.1
Move the leading negative in into the numerator.
Step 5.3.2.1.1.2
Factor out of .
Step 5.3.2.1.1.3
Cancel the common factor.
Step 5.3.2.1.1.4
Rewrite the expression.
Step 5.3.2.1.2
Move the negative in front of the fraction.
Step 5.4
Divide each term in by and simplify.
Step 5.4.1
Divide each term in by .
Step 5.4.2
Simplify the left side.
Step 5.4.2.1
Cancel the common factor of .
Step 5.4.2.1.1
Cancel the common factor.
Step 5.4.2.1.2
Divide by .
Step 5.4.3
Simplify the right side.
Step 5.4.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.4.3.2
Multiply by .
Step 5.4.3.3
Move to the left of .
Step 6
Replace with .