Calculus Examples

Find the Derivative - d/dx y=((x-4)/(3-x^2))^3
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
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
Since is constant with respect to , the derivative of with respect to is .
Step 3.7
Add and .
Step 3.8
Since is constant with respect to , the derivative of with respect to is .
Step 3.9
Multiply.
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Step 3.9.1
Multiply by .
Step 3.9.2
Multiply by .
Step 3.10
Differentiate using the Power Rule which states that is where .
Step 3.11
Combine fractions.
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Step 3.11.1
Move to the left of .
Step 3.11.2
Combine and .
Step 3.11.3
Move to the left of .
Step 4
Simplify.
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Step 4.1
Apply the product rule to .
Step 4.2
Apply the distributive property.
Step 4.3
Apply the distributive property.
Step 4.4
Apply the distributive property.
Step 4.5
Combine terms.
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Step 4.5.1
Multiply by .
Step 4.5.2
Multiply by .
Step 4.5.3
Raise to the power of .
Step 4.5.4
Raise to the power of .
Step 4.5.5
Use the power rule to combine exponents.
Step 4.5.6
Add and .
Step 4.5.7
Multiply by .
Step 4.5.8
Multiply by .
Step 4.5.9
Multiply by .
Step 4.5.10
Add and .
Step 4.5.11
Multiply by .
Step 4.5.12
Multiply by by adding the exponents.
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Step 4.5.12.1
Use the power rule to combine exponents.
Step 4.5.12.2
Add and .
Step 4.6
Reorder terms.
Step 4.7
Simplify the numerator.
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Step 4.7.1
Factor out of .
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Step 4.7.1.1
Factor out of .
Step 4.7.1.2
Factor out of .
Step 4.7.1.3
Factor out of .
Step 4.7.1.4
Factor out of .
Step 4.7.2
Reorder terms.
Step 4.8
Move to the left of .