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Calculus Examples
Step 1
Step 1.1
Combine and .
Step 1.2
Use to rewrite as .
Step 2
Differentiate using the Product Rule which states that is where and .
Step 3
Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4
Simplify the expression.
Step 3.4.1
Add and .
Step 3.4.2
Multiply by .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Multiply by .
Step 11
Step 11.1
Multiply by .
Step 11.2
Move to the denominator using the negative exponent rule .
Step 12
To write as a fraction with a common denominator, multiply by .
Step 13
Combine and .
Step 14
Combine the numerators over the common denominator.
Step 15
Combine and .
Step 16
Factor out of .
Step 17
Step 17.1
Factor out of .
Step 17.2
Cancel the common factor.
Step 17.3
Rewrite the expression.
Step 18
Step 18.1
Apply the distributive property.
Step 18.2
Simplify the numerator.
Step 18.2.1
Simplify each term.
Step 18.2.1.1
Combine and .
Step 18.2.1.2
Move to the numerator using the negative exponent rule .
Step 18.2.1.3
Multiply by by adding the exponents.
Step 18.2.1.3.1
Multiply by .
Step 18.2.1.3.1.1
Raise to the power of .
Step 18.2.1.3.1.2
Use the power rule to combine exponents.
Step 18.2.1.3.2
Write as a fraction with a common denominator.
Step 18.2.1.3.3
Combine the numerators over the common denominator.
Step 18.2.1.3.4
Subtract from .
Step 18.2.1.4
Combine and .
Step 18.2.1.5
Move the negative in front of the fraction.
Step 18.2.2
To write as a fraction with a common denominator, multiply by .
Step 18.2.3
Combine and .
Step 18.2.4
Combine the numerators over the common denominator.
Step 18.2.5
Add and .
Step 18.2.5.1
Reorder and .
Step 18.2.5.2
Add and .
Step 18.3
Combine terms.
Step 18.3.1
Multiply by .
Step 18.3.2
Combine.
Step 18.3.3
Apply the distributive property.
Step 18.3.4
Cancel the common factor of .
Step 18.3.4.1
Cancel the common factor.
Step 18.3.4.2
Rewrite the expression.
Step 18.3.5
Multiply by .
Step 18.3.6
Combine and .
Step 18.3.7
Multiply by .
Step 18.3.8
Factor out of .
Step 18.3.9
Cancel the common factors.
Step 18.3.9.1
Factor out of .
Step 18.3.9.2
Cancel the common factor.
Step 18.3.9.3
Rewrite the expression.
Step 18.3.10
Move the negative in front of the fraction.
Step 18.3.11
Multiply by .
Step 18.3.12
Factor out of .
Step 18.3.13
Factor out of .
Step 18.3.14
Factor out of .
Step 18.3.15
Cancel the common factors.
Step 18.3.15.1
Factor out of .
Step 18.3.15.2
Cancel the common factor.
Step 18.3.15.3
Rewrite the expression.
Step 18.4
Simplify the numerator.
Step 18.4.1
To write as a fraction with a common denominator, multiply by .
Step 18.4.2
Combine the numerators over the common denominator.
Step 18.4.3
Simplify the numerator.
Step 18.4.3.1
Multiply by by adding the exponents.
Step 18.4.3.1.1
Use the power rule to combine exponents.
Step 18.4.3.1.2
Combine the numerators over the common denominator.
Step 18.4.3.1.3
Add and .
Step 18.4.3.1.4
Divide by .
Step 18.4.3.2
Simplify .
Step 18.5
Multiply the numerator by the reciprocal of the denominator.
Step 18.6
Multiply by .
Step 18.7
Move to the left of .