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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Differentiate both sides of the equation.
Step 3
The derivative of with respect to is .
Step 4
Step 4.1
Differentiate using the Quotient Rule which states that is where and .
Step 4.2
Differentiate using the Power Rule which states that is where .
Step 4.3
To write as a fraction with a common denominator, multiply by .
Step 4.4
Combine and .
Step 4.5
Combine the numerators over the common denominator.
Step 4.6
Simplify the numerator.
Step 4.6.1
Multiply by .
Step 4.6.2
Subtract from .
Step 4.7
Combine fractions.
Step 4.7.1
Move the negative in front of the fraction.
Step 4.7.2
Combine and .
Step 4.7.3
Move to the denominator using the negative exponent rule .
Step 4.8
By the Sum Rule, the derivative of with respect to is .
Step 4.9
Since is constant with respect to , the derivative of with respect to is .
Step 4.10
Add and .
Step 4.11
Since is constant with respect to , the derivative of with respect to is .
Step 4.12
Multiply.
Step 4.12.1
Multiply by .
Step 4.12.2
Multiply by .
Step 4.13
Differentiate using the Power Rule which states that is where .
Step 4.14
Multiply by .
Step 4.15
Simplify.
Step 4.15.1
Apply the distributive property.
Step 4.15.2
Simplify the numerator.
Step 4.15.2.1
Simplify each term.
Step 4.15.2.1.1
Multiply by .
Step 4.15.2.1.2
Combine and .
Step 4.15.2.1.3
Move to the numerator using the negative exponent rule .
Step 4.15.2.1.4
Multiply by by adding the exponents.
Step 4.15.2.1.4.1
Multiply by .
Step 4.15.2.1.4.1.1
Raise to the power of .
Step 4.15.2.1.4.1.2
Use the power rule to combine exponents.
Step 4.15.2.1.4.2
Write as a fraction with a common denominator.
Step 4.15.2.1.4.3
Combine the numerators over the common denominator.
Step 4.15.2.1.4.4
Subtract from .
Step 4.15.2.2
To write as a fraction with a common denominator, multiply by .
Step 4.15.2.3
Combine and .
Step 4.15.2.4
Combine the numerators over the common denominator.
Step 4.15.2.5
Add and .
Step 4.15.2.5.1
Reorder and .
Step 4.15.2.5.2
Add and .
Step 4.15.3
Combine terms.
Step 4.15.3.1
Multiply by .
Step 4.15.3.2
Combine.
Step 4.15.3.3
Apply the distributive property.
Step 4.15.3.4
Cancel the common factor of .
Step 4.15.3.4.1
Cancel the common factor.
Step 4.15.3.4.2
Rewrite the expression.
Step 4.15.3.5
Cancel the common factor of .
Step 4.15.3.5.1
Factor out of .
Step 4.15.3.5.2
Cancel the common factor.
Step 4.15.3.5.3
Rewrite the expression.
Step 4.15.3.6
Multiply by by adding the exponents.
Step 4.15.3.6.1
Use the power rule to combine exponents.
Step 4.15.3.6.2
Combine the numerators over the common denominator.
Step 4.15.3.6.3
Add and .
Step 4.15.3.6.4
Divide by .
Step 4.15.3.7
Simplify .
Step 4.15.4
Reorder terms.
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .