Calculus Examples

Find the Derivative - d/dx (-8x)/(x^2+1)
Step 1
Differentiate using the Constant Multiple Rule.
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Step 1.1
Move the negative in front of the fraction.
Step 1.2
Since is constant with respect to , the derivative of with respect to is .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
Differentiate using the Power Rule which states that is where .
Step 3.2
Multiply by .
Step 3.3
By the Sum Rule, the derivative of with respect to is .
Step 3.4
Differentiate using the Power Rule which states that is where .
Step 3.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.6
Simplify the expression.
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Step 3.6.1
Add and .
Step 3.6.2
Multiply by .
Step 4
Raise to the power of .
Step 5
Raise to the power of .
Step 6
Use the power rule to combine exponents.
Step 7
Add and .
Step 8
Subtract from .
Step 9
Combine and .
Step 10
Move the negative in front of the fraction.
Step 11
Simplify.
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Step 11.1
Apply the distributive property.
Step 11.2
Simplify each term.
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Step 11.2.1
Multiply by .
Step 11.2.2
Multiply by .