Calculus Examples

Find dy/dx x/y=1/9
Step 1
Differentiate both sides of the equation.
Step 2
Differentiate the left side of the equation.
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Step 2.1
Differentiate using the Quotient Rule which states that is where and .
Step 2.2
Differentiate using the Power Rule.
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Step 2.2.1
Differentiate using the Power Rule which states that is where .
Step 2.2.2
Multiply by .
Step 2.3
Rewrite as .
Step 2.4
Reorder terms.
Step 3
Since is constant with respect to , the derivative of with respect to is .
Step 4
Reform the equation by setting the left side equal to the right side.
Step 5
Solve for .
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Step 5.1
Set the numerator equal to zero.
Step 5.2
Solve the equation for .
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Divide each term in by and simplify.
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Step 5.2.2.1
Divide each term in by .
Step 5.2.2.2
Simplify the left side.
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Step 5.2.2.2.1
Dividing two negative values results in a positive value.
Step 5.2.2.2.2
Cancel the common factor of .
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Step 5.2.2.2.2.1
Cancel the common factor.
Step 5.2.2.2.2.2
Divide by .
Step 5.2.2.3
Simplify the right side.
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Step 5.2.2.3.1
Dividing two negative values results in a positive value.
Step 6
Replace with .