Calculus Examples

Find the Derivative - d/dx y=8/x-x/8
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Rewrite as .
Step 2.3
Differentiate using the Power Rule which states that is where .
Step 2.4
Multiply by .
Step 3
Evaluate .
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Multiply by .
Step 4
Simplify.
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Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Combine terms.
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Step 4.2.1
Combine and .
Step 4.2.2
Move the negative in front of the fraction.