Calculus Examples

Find the Derivative - d/dx y=(7-x^2)(x^3-x+5)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Differentiate using the Power Rule which states that is where .
Step 2.5
Multiply by .
Step 2.6
Since is constant with respect to , the derivative of with respect to is .
Step 2.7
Add and .
Step 2.8
By the Sum Rule, the derivative of with respect to is .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Add and .
Step 2.11
Since is constant with respect to , the derivative of with respect to is .
Step 2.12
Differentiate using the Power Rule which states that is where .
Step 2.13
Multiply by .
Step 3
Simplify.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 3.4
Apply the distributive property.
Step 3.5
Combine terms.
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Step 3.5.1
Multiply by .
Step 3.5.2
Multiply by .
Step 3.5.3
Multiply by by adding the exponents.
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Step 3.5.3.1
Move .
Step 3.5.3.2
Use the power rule to combine exponents.
Step 3.5.3.3
Add and .
Step 3.5.4
Multiply by .
Step 3.5.5
Multiply by .
Step 3.5.6
Multiply by .
Step 3.5.7
Add and .
Step 3.5.8
Multiply by by adding the exponents.
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Step 3.5.8.1
Move .
Step 3.5.8.2
Multiply by .
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Step 3.5.8.2.1
Raise to the power of .
Step 3.5.8.2.2
Use the power rule to combine exponents.
Step 3.5.8.3
Add and .
Step 3.5.9
Move to the left of .
Step 3.5.10
Multiply by .
Step 3.5.11
Raise to the power of .
Step 3.5.12
Raise to the power of .
Step 3.5.13
Use the power rule to combine exponents.
Step 3.5.14
Add and .
Step 3.5.15
Multiply by .
Step 3.5.16
Subtract from .
Step 3.5.17
Add and .
Step 3.6
Reorder terms.