Calculus Examples

Find dy/dx (y-3)^2=4(x-5)
Step 1
Differentiate both sides of the equation.
Step 2
Differentiate the left side of the equation.
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Step 2.1
Rewrite as .
Step 2.2
Expand using the FOIL Method.
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Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply by .
Step 2.3.1.2
Move to the left of .
Step 2.3.1.3
Multiply by .
Step 2.3.2
Subtract from .
Step 2.4
By the Sum Rule, the derivative of with respect to is .
Step 2.5
Differentiate using the chain rule, which states that is where and .
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Step 2.5.1
To apply the Chain Rule, set as .
Step 2.5.2
Differentiate using the Power Rule which states that is where .
Step 2.5.3
Replace all occurrences of with .
Step 2.6
Rewrite as .
Step 2.7
Since is constant with respect to , the derivative of with respect to is .
Step 2.8
Rewrite as .
Step 2.9
Since is constant with respect to , the derivative of with respect to is .
Step 2.10
Add and .
Step 3
Differentiate the right side of the equation.
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Step 3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.2
By the Sum Rule, the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Simplify the expression.
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Step 3.5.1
Add and .
Step 3.5.2
Multiply by .
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
Factor out of .
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Step 5.1.1
Factor out of .
Step 5.1.2
Factor out of .
Step 5.1.3
Factor out of .
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Rewrite the expression.
Step 5.2.2.2
Cancel the common factor of .
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Step 5.2.2.2.1
Cancel the common factor.
Step 5.2.2.2.2
Divide by .
Step 5.2.3
Simplify the right side.
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Step 5.2.3.1
Cancel the common factor of and .
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Step 5.2.3.1.1
Factor out of .
Step 5.2.3.1.2
Cancel the common factors.
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Step 5.2.3.1.2.1
Cancel the common factor.
Step 5.2.3.1.2.2
Rewrite the expression.
Step 6
Replace with .