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Calculus Examples
Step 1
Step 1.1
Use to rewrite as .
Step 1.2
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Step 3.1
Apply the power rule and multiply exponents, .
Step 3.2
Cancel the common factor of .
Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 4
Simplify.
Step 5
Step 5.1
Differentiate using the Power Rule which states that is where .
Step 5.2
Move to the left of .
Step 6
Step 6.1
To apply the Chain Rule, set as .
Step 6.2
Differentiate using the Power Rule which states that is where .
Step 6.3
Replace all occurrences of with .
Step 7
To write as a fraction with a common denominator, multiply by .
Step 8
Combine and .
Step 9
Combine the numerators over the common denominator.
Step 10
Step 10.1
Multiply by .
Step 10.2
Subtract from .
Step 11
Step 11.1
Move the negative in front of the fraction.
Step 11.2
Combine and .
Step 11.3
Move to the denominator using the negative exponent rule .
Step 11.4
Combine and .
Step 12
By the Sum Rule, the derivative of with respect to is .
Step 13
Differentiate using the Power Rule which states that is where .
Step 14
Since is constant with respect to , the derivative of with respect to is .
Step 15
Step 15.1
Add and .
Step 15.2
Multiply by .
Step 15.3
Combine and .
Step 15.4
Combine and .
Step 16
Raise to the power of .
Step 17
Use the power rule to combine exponents.
Step 18
Add and .
Step 19
Factor out of .
Step 20
Step 20.1
Factor out of .
Step 20.2
Cancel the common factor.
Step 20.3
Rewrite the expression.
Step 21
Move the negative in front of the fraction.
Step 22
Step 22.1
Move .
Step 22.2
To write as a fraction with a common denominator, multiply by .
Step 22.3
Combine the numerators over the common denominator.
Step 23
Step 23.1
Move .
Step 23.2
Use the power rule to combine exponents.
Step 23.3
Combine the numerators over the common denominator.
Step 23.4
Add and .
Step 23.5
Divide by .
Step 24
Simplify .
Step 25
Rewrite as a product.
Step 26
Multiply by .
Step 27
Step 27.1
Multiply by .
Step 27.1.1
Raise to the power of .
Step 27.1.2
Use the power rule to combine exponents.
Step 27.2
Write as a fraction with a common denominator.
Step 27.3
Combine the numerators over the common denominator.
Step 27.4
Add and .
Step 28
Combine and .
Step 29
Step 29.1
Apply the distributive property.
Step 29.2
Apply the distributive property.
Step 29.3
Simplify the numerator.
Step 29.3.1
Simplify each term.
Step 29.3.1.1
Multiply by by adding the exponents.
Step 29.3.1.1.1
Move .
Step 29.3.1.1.2
Multiply by .
Step 29.3.1.1.2.1
Raise to the power of .
Step 29.3.1.1.2.2
Use the power rule to combine exponents.
Step 29.3.1.1.3
Add and .
Step 29.3.1.2
Multiply by .
Step 29.3.1.3
Multiply by .
Step 29.3.1.4
Multiply by .
Step 29.3.1.5
Multiply by .
Step 29.3.2
Subtract from .
Step 29.4
Factor out of .
Step 29.4.1
Factor out of .
Step 29.4.2
Factor out of .
Step 29.4.3
Factor out of .