Calculus Examples

Find the Derivative - d/dx y=(2x^7-x^2)((x-1)/(x+1))
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate.
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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.
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Step 3.4.1
Add and .
Step 3.4.2
Multiply by .
Step 3.5
By the Sum Rule, the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.8
Simplify the expression.
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Step 3.8.1
Add and .
Step 3.8.2
Multiply by .
Step 3.9
By the Sum Rule, the derivative of with respect to is .
Step 3.10
Since is constant with respect to , the derivative of with respect to is .
Step 3.11
Differentiate using the Power Rule which states that is where .
Step 3.12
Multiply by .
Step 3.13
Since is constant with respect to , the derivative of with respect to is .
Step 3.14
Differentiate using the Power Rule which states that is where .
Step 3.15
Multiply by .
Step 4
Simplify.
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Step 4.1
Apply the distributive property.
Step 4.2
Combine terms.
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Step 4.2.1
Multiply by .
Step 4.2.2
Subtract from .
Step 4.2.3
Add and .
Step 4.2.4
Add and .
Step 4.3
Reorder terms.
Step 4.4
Simplify each term.
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Step 4.4.1
Multiply by .
Step 4.4.2
Factor out of .
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Step 4.4.2.1
Factor out of .
Step 4.4.2.2
Factor out of .
Step 4.4.2.3
Factor out of .
Step 4.4.3
Move to the left of .
Step 4.4.4
Multiply by .
Step 4.4.5
Factor out of .
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Step 4.4.5.1
Factor out of .
Step 4.4.5.2
Factor out of .
Step 4.4.5.3
Factor out of .
Step 4.5
To write as a fraction with a common denominator, multiply by .
Step 4.6
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.6.1
Multiply by .
Step 4.6.2
Raise to the power of .
Step 4.6.3
Raise to the power of .
Step 4.6.4
Use the power rule to combine exponents.
Step 4.6.5
Add and .
Step 4.7
Combine the numerators over the common denominator.
Step 4.8
Simplify the numerator.
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Step 4.8.1
Factor out of .
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Step 4.8.1.1
Factor out of .
Step 4.8.1.2
Factor out of .
Step 4.8.1.3
Factor out of .
Step 4.8.2
Apply the distributive property.
Step 4.8.3
Rewrite using the commutative property of multiplication.
Step 4.8.4
Move to the left of .
Step 4.8.5
Simplify each term.
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Step 4.8.5.1
Multiply by by adding the exponents.
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Step 4.8.5.1.1
Move .
Step 4.8.5.1.2
Multiply by .
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Step 4.8.5.1.2.1
Raise to the power of .
Step 4.8.5.1.2.2
Use the power rule to combine exponents.
Step 4.8.5.1.3
Add and .
Step 4.8.5.2
Rewrite as .
Step 4.8.6
Expand using the FOIL Method.
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Step 4.8.6.1
Apply the distributive property.
Step 4.8.6.2
Apply the distributive property.
Step 4.8.6.3
Apply the distributive property.
Step 4.8.7
Simplify each term.
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Step 4.8.7.1
Multiply by by adding the exponents.
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Step 4.8.7.1.1
Move .
Step 4.8.7.1.2
Multiply by .
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Step 4.8.7.1.2.1
Raise to the power of .
Step 4.8.7.1.2.2
Use the power rule to combine exponents.
Step 4.8.7.1.3
Add and .
Step 4.8.7.2
Multiply by .
Step 4.8.7.3
Rewrite as .
Step 4.8.7.4
Multiply by .
Step 4.8.8
Expand by multiplying each term in the first expression by each term in the second expression.
Step 4.8.9
Simplify each term.
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Step 4.8.9.1
Multiply by by adding the exponents.
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Step 4.8.9.1.1
Move .
Step 4.8.9.1.2
Multiply by .
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Step 4.8.9.1.2.1
Raise to the power of .
Step 4.8.9.1.2.2
Use the power rule to combine exponents.
Step 4.8.9.1.3
Add and .
Step 4.8.9.2
Multiply by .
Step 4.8.9.3
Multiply by by adding the exponents.
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Step 4.8.9.3.1
Move .
Step 4.8.9.3.2
Multiply by .
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Step 4.8.9.3.2.1
Raise to the power of .
Step 4.8.9.3.2.2
Use the power rule to combine exponents.
Step 4.8.9.3.3
Add and .
Step 4.8.9.4
Multiply by .
Step 4.8.9.5
Multiply by by adding the exponents.
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Step 4.8.9.5.1
Move .
Step 4.8.9.5.2
Multiply by .
Step 4.8.9.6
Multiply by .
Step 4.8.9.7
Multiply by .
Step 4.8.9.8
Multiply by .
Step 4.8.10
Combine the opposite terms in .
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Step 4.8.10.1
Subtract from .
Step 4.8.10.2
Add and .
Step 4.8.10.3
Add and .
Step 4.8.10.4
Add and .
Step 4.8.11
Reorder terms.