Find dx/dy 2x^3y+3xy^3=5

Math
Differentiate both sides of the equation.
Differentiate the left side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Differentiate using the Power Rule which states that is where .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Multiply by .
Move to the left of .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Differentiate using the Power Rule which states that is where .
Rewrite as .
Move to the left of .
Simplify.
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Apply the distributive property.
Apply the distributive property.
Combine terms.
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Multiply by .
Multiply by .
Reorder terms.
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Solve for .
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Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
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Divide each term in by .
Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Simplify each term.
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Move the negative in front of the fraction.
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Multiply by .
Multiply by .
Simplify with factoring out.
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Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
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Rewrite as .
Move the negative in front of the fraction.
Replace with .
Find dx/dy 2x^3y+3xy^3=5


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