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Calculus Examples
Step 1
Use to rewrite as .
Step 2
Step 2.1
To apply the Chain Rule, set as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Combine and .
Step 5
Combine the numerators over the common denominator.
Step 6
Step 6.1
Multiply by .
Step 6.2
Subtract from .
Step 7
Move the negative in front of the fraction.
Step 8
Differentiate using the Quotient Rule which states that is where and .
Step 9
Step 9.1
By the Sum Rule, the derivative of with respect to is .
Step 9.2
Since is constant with respect to , the derivative of with respect to is .
Step 9.3
Add and .
Step 9.4
Since is constant with respect to , the derivative of with respect to is .
Step 9.5
Differentiate using the Power Rule which states that is where .
Step 9.6
Simplify the expression.
Step 9.6.1
Multiply by .
Step 9.6.2
Move to the left of .
Step 9.7
By the Sum Rule, the derivative of with respect to is .
Step 9.8
Since is constant with respect to , the derivative of with respect to is .
Step 9.9
Add and .
Step 9.10
Since is constant with respect to , the derivative of with respect to is .
Step 9.11
Multiply by .
Step 9.12
Differentiate using the Power Rule which states that is where .
Step 9.13
Simplify terms.
Step 9.13.1
Multiply by .
Step 9.13.2
Multiply by .
Step 9.13.3
Move to the left of .
Step 9.13.4
Cancel the common factor of and .
Step 9.13.4.1
Factor out of .
Step 9.13.4.2
Factor out of .
Step 9.13.4.3
Factor out of .
Step 9.13.4.4
Cancel the common factors.
Step 9.13.4.4.1
Factor out of .
Step 9.13.4.4.2
Cancel the common factor.
Step 9.13.4.4.3
Rewrite the expression.
Step 10
Step 10.1
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 10.2
Apply the product rule to .
Step 10.3
Apply the distributive property.
Step 10.4
Apply the distributive property.
Step 10.5
Combine terms.
Step 10.5.1
Multiply by .
Step 10.5.2
Multiply by .
Step 10.5.3
Multiply by .
Step 10.5.4
Multiply by .
Step 10.5.5
Subtract from .
Step 10.5.6
Add and .
Step 10.5.7
Subtract from .
Step 10.5.8
Move the negative in front of the fraction.
Step 10.5.9
Multiply by .
Step 10.5.10
Move to the left of .
Step 10.5.11
Move to the denominator using the negative exponent rule .
Step 10.5.12
Multiply by by adding the exponents.
Step 10.5.12.1
Move .
Step 10.5.12.2
Use the power rule to combine exponents.
Step 10.5.12.3
To write as a fraction with a common denominator, multiply by .
Step 10.5.12.4
Combine and .
Step 10.5.12.5
Combine the numerators over the common denominator.
Step 10.5.12.6
Simplify the numerator.
Step 10.5.12.6.1
Multiply by .
Step 10.5.12.6.2
Add and .