Calculus Examples

Find the Derivative - d/dx x^(4/5)(x-9)^2
Step 1
Rewrite as .
Step 2
Expand using the FOIL Method.
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Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify and combine like terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Multiply by .
Step 3.1.2
Move to the left of .
Step 3.1.3
Multiply by .
Step 3.2
Subtract from .
Step 4
Differentiate using the Product Rule which states that is where and .
Step 5
Differentiate.
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Step 5.1
By the Sum Rule, the derivative of with respect to is .
Step 5.2
Differentiate using the Power Rule which states that is where .
Step 5.3
Since is constant with respect to , the derivative of with respect to is .
Step 5.4
Differentiate using the Power Rule which states that is where .
Step 5.5
Multiply by .
Step 5.6
Since is constant with respect to , the derivative of with respect to is .
Step 5.7
Add and .
Step 5.8
Differentiate using the Power Rule which states that is where .
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Simplify the numerator.
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Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Move the negative in front of the fraction.
Step 11
Combine and .
Step 12
Move to the denominator using the negative exponent rule .
Step 13
Simplify.
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Step 13.1
Apply the distributive property.
Step 13.2
Apply the distributive property.
Step 13.3
Combine terms.
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Step 13.3.1
Multiply by by adding the exponents.
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Step 13.3.1.1
Move .
Step 13.3.1.2
Multiply by .
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Step 13.3.1.2.1
Raise to the power of .
Step 13.3.1.2.2
Use the power rule to combine exponents.
Step 13.3.1.3
Write as a fraction with a common denominator.
Step 13.3.1.4
Combine the numerators over the common denominator.
Step 13.3.1.5
Add and .
Step 13.3.2
Move to the left of .
Step 13.3.3
Move to the left of .
Step 13.3.4
Combine and .
Step 13.3.5
Move to the left of .
Step 13.3.6
Move to the numerator using the negative exponent rule .
Step 13.3.7
Multiply by by adding the exponents.
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Step 13.3.7.1
Move .
Step 13.3.7.2
Use the power rule to combine exponents.
Step 13.3.7.3
To write as a fraction with a common denominator, multiply by .
Step 13.3.7.4
Combine and .
Step 13.3.7.5
Combine the numerators over the common denominator.
Step 13.3.7.6
Simplify the numerator.
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Step 13.3.7.6.1
Multiply by .
Step 13.3.7.6.2
Add and .
Step 13.3.8
Combine and .
Step 13.3.9
Multiply by .
Step 13.3.10
Combine and .
Step 13.3.11
Move to the left of .
Step 13.3.12
Move to the numerator using the negative exponent rule .
Step 13.3.13
Multiply by by adding the exponents.
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Step 13.3.13.1
Move .
Step 13.3.13.2
Multiply by .
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Step 13.3.13.2.1
Raise to the power of .
Step 13.3.13.2.2
Use the power rule to combine exponents.
Step 13.3.13.3
Write as a fraction with a common denominator.
Step 13.3.13.4
Combine the numerators over the common denominator.
Step 13.3.13.5
Add and .
Step 13.3.14
Move the negative in front of the fraction.
Step 13.3.15
Combine and .
Step 13.3.16
Multiply by .
Step 13.3.17
To write as a fraction with a common denominator, multiply by .
Step 13.3.18
Combine and .
Step 13.3.19
Combine the numerators over the common denominator.
Step 13.3.20
Multiply by .
Step 13.3.21
Add and .
Step 13.3.22
To write as a fraction with a common denominator, multiply by .
Step 13.3.23
Combine and .
Step 13.3.24
Combine the numerators over the common denominator.
Step 13.3.25
Multiply by .
Step 13.3.26
Subtract from .
Step 13.3.27
Move the negative in front of the fraction.
Step 13.4
Reorder terms.