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Calculus Examples
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
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.
Step 4.2.1
By the Sum Rule, the derivative of with respect to is .
Step 4.2.2
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
Since is constant with respect to , the derivative of with respect to is .
Step 4.9
Add and .
Step 4.10
By the Sum Rule, the derivative of with respect to is .
Step 4.11
Differentiate using the Power Rule which states that is where .
Step 4.12
To write as a fraction with a common denominator, multiply by .
Step 4.13
Combine and .
Step 4.14
Combine the numerators over the common denominator.
Step 4.15
Simplify the numerator.
Step 4.15.1
Multiply by .
Step 4.15.2
Subtract from .
Step 4.16
Combine fractions.
Step 4.16.1
Move the negative in front of the fraction.
Step 4.16.2
Combine and .
Step 4.16.3
Move to the denominator using the negative exponent rule .
Step 4.17
Since is constant with respect to , the derivative of with respect to is .
Step 4.18
Add and .
Step 4.19
Simplify.
Step 4.19.1
Apply the distributive property.
Step 4.19.2
Apply the distributive property.
Step 4.19.3
Apply the distributive property.
Step 4.19.4
Simplify the numerator.
Step 4.19.4.1
Combine the opposite terms in .
Step 4.19.4.1.1
Subtract from .
Step 4.19.4.1.2
Add and .
Step 4.19.4.2
Simplify each term.
Step 4.19.4.2.1
Cancel the common factor of .
Step 4.19.4.2.1.1
Factor out of .
Step 4.19.4.2.1.2
Cancel the common factor.
Step 4.19.4.2.1.3
Rewrite the expression.
Step 4.19.4.2.2
Combine and .
Step 4.19.4.2.3
Multiply by .
Step 4.19.4.2.4
Cancel the common factor of .
Step 4.19.4.2.4.1
Factor out of .
Step 4.19.4.2.4.2
Cancel the common factor.
Step 4.19.4.2.4.3
Rewrite the expression.
Step 4.19.4.2.5
Combine and .
Step 4.19.4.3
Combine the numerators over the common denominator.
Step 4.19.4.4
Add and .
Step 4.19.5
Combine terms.
Step 4.19.5.1
Rewrite as a product.
Step 4.19.5.2
Multiply by .
Step 5
Reform the equation by setting the left side equal to the right side.
Step 6
Replace with .