Calculus Examples

Find the Derivative - d/dx y=(x^6)/(1-x^5)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
Differentiate using the Power Rule which states that is where .
Step 2.2
Move to the left of .
Step 2.3
By the Sum Rule, the derivative of with respect to is .
Step 2.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.5
Add and .
Step 2.6
Since is constant with respect to , the derivative of with respect to is .
Step 2.7
Multiply.
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Step 2.7.1
Multiply by .
Step 2.7.2
Multiply by .
Step 2.8
Differentiate using the Power Rule which states that is where .
Step 3
Multiply by by adding the exponents.
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Step 3.1
Move .
Step 3.2
Use the power rule to combine exponents.
Step 3.3
Add and .
Step 4
Move to the left of .
Step 5
Simplify.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Simplify the numerator.
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Step 5.3.1
Simplify each term.
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Step 5.3.1.1
Multiply by .
Step 5.3.1.2
Multiply by by adding the exponents.
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Step 5.3.1.2.1
Move .
Step 5.3.1.2.2
Use the power rule to combine exponents.
Step 5.3.1.2.3
Add and .
Step 5.3.1.3
Multiply by .
Step 5.3.2
Add and .
Step 5.4
Reorder terms.
Step 5.5
Factor out of .
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Step 5.5.1
Factor out of .
Step 5.5.2
Factor out of .
Step 5.5.3
Factor out of .
Step 5.6
Factor out of .
Step 5.7
Rewrite as .
Step 5.8
Factor out of .
Step 5.9
Rewrite as .
Step 5.10
Move the negative in front of the fraction.