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Calculus Examples
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Multiply by .
Step 2.5
Since is constant with respect to , the derivative of with respect to is .
Step 2.6
Differentiate using the Power Rule which states that is where .
Step 2.7
Multiply by .
Step 2.8
By the Sum Rule, the derivative of with respect to is .
Step 2.9
Differentiate using the Power Rule which states that is where .
Step 2.10
Differentiate using the Power Rule which states that is where .
Step 3
Step 3.1
Reorder terms.
Step 3.2
Simplify each term.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Rewrite the expression using the negative exponent rule .
Step 3.2.1.2
Combine and .
Step 3.2.1.3
Move the negative in front of the fraction.
Step 3.2.1.4
Rewrite the expression using the negative exponent rule .
Step 3.2.1.5
Combine and .
Step 3.2.2
Simplify each term.
Step 3.2.2.1
Rewrite the expression using the negative exponent rule .
Step 3.2.2.2
Rewrite the expression using the negative exponent rule .
Step 3.2.3
Expand using the FOIL Method.
Step 3.2.3.1
Apply the distributive property.
Step 3.2.3.2
Apply the distributive property.
Step 3.2.3.3
Apply the distributive property.
Step 3.2.4
Simplify and combine like terms.
Step 3.2.4.1
Simplify each term.
Step 3.2.4.1.1
Multiply .
Step 3.2.4.1.1.1
Multiply by .
Step 3.2.4.1.1.2
Multiply by by adding the exponents.
Step 3.2.4.1.1.2.1
Multiply by .
Step 3.2.4.1.1.2.1.1
Raise to the power of .
Step 3.2.4.1.1.2.1.2
Use the power rule to combine exponents.
Step 3.2.4.1.1.2.2
Add and .
Step 3.2.4.1.2
Multiply .
Step 3.2.4.1.2.1
Multiply by .
Step 3.2.4.1.2.2
Multiply by by adding the exponents.
Step 3.2.4.1.2.2.1
Use the power rule to combine exponents.
Step 3.2.4.1.2.2.2
Add and .
Step 3.2.4.1.3
Combine.
Step 3.2.4.1.4
Multiply by by adding the exponents.
Step 3.2.4.1.4.1
Multiply by .
Step 3.2.4.1.4.1.1
Raise to the power of .
Step 3.2.4.1.4.1.2
Use the power rule to combine exponents.
Step 3.2.4.1.4.2
Add and .
Step 3.2.4.1.5
Multiply by .
Step 3.2.4.1.6
Combine.
Step 3.2.4.1.7
Multiply by by adding the exponents.
Step 3.2.4.1.7.1
Use the power rule to combine exponents.
Step 3.2.4.1.7.2
Add and .
Step 3.2.4.1.8
Multiply by .
Step 3.2.4.2
Combine the numerators over the common denominator.
Step 3.2.4.3
Add and .
Step 3.2.5
Simplify each term.
Step 3.2.5.1
Rewrite the expression using the negative exponent rule .
Step 3.2.5.2
Rewrite the expression using the negative exponent rule .
Step 3.2.5.3
Combine and .
Step 3.2.5.4
Move the negative in front of the fraction.
Step 3.2.6
Simplify each term.
Step 3.2.6.1
Rewrite the expression using the negative exponent rule .
Step 3.2.6.2
Combine and .
Step 3.2.6.3
Rewrite the expression using the negative exponent rule .
Step 3.2.6.4
Combine and .
Step 3.2.6.5
Move the negative in front of the fraction.
Step 3.2.7
Expand using the FOIL Method.
Step 3.2.7.1
Apply the distributive property.
Step 3.2.7.2
Apply the distributive property.
Step 3.2.7.3
Apply the distributive property.
Step 3.2.8
Simplify and combine like terms.
Step 3.2.8.1
Simplify each term.
Step 3.2.8.1.1
Multiply .
Step 3.2.8.1.1.1
Multiply by .
Step 3.2.8.1.1.2
Multiply by by adding the exponents.
Step 3.2.8.1.1.2.1
Use the power rule to combine exponents.
Step 3.2.8.1.1.2.2
Add and .
Step 3.2.8.1.2
Multiply .
Step 3.2.8.1.2.1
Multiply by .
Step 3.2.8.1.2.2
Multiply by .
Step 3.2.8.1.2.3
Multiply by .
Step 3.2.8.1.2.4
Multiply by by adding the exponents.
Step 3.2.8.1.2.4.1
Use the power rule to combine exponents.
Step 3.2.8.1.2.4.2
Add and .
Step 3.2.8.1.3
Multiply .
Step 3.2.8.1.3.1
Multiply by .
Step 3.2.8.1.3.2
Multiply by .
Step 3.2.8.1.3.3
Multiply by by adding the exponents.
Step 3.2.8.1.3.3.1
Use the power rule to combine exponents.
Step 3.2.8.1.3.3.2
Add and .
Step 3.2.8.1.4
Multiply .
Step 3.2.8.1.4.1
Multiply by .
Step 3.2.8.1.4.2
Multiply by .
Step 3.2.8.1.4.3
Multiply by .
Step 3.2.8.1.4.4
Multiply by .
Step 3.2.8.1.4.5
Multiply by by adding the exponents.
Step 3.2.8.1.4.5.1
Use the power rule to combine exponents.
Step 3.2.8.1.4.5.2
Add and .
Step 3.2.8.2
Combine the numerators over the common denominator.
Step 3.2.8.3
Subtract from .
Step 3.2.9
Move the negative in front of the fraction.
Step 3.3
Combine the numerators over the common denominator.
Step 3.4
Subtract from .
Step 3.5
Subtract from .
Step 3.6
Add and .
Step 3.7
Move the negative in front of the fraction.