Find ds/dy s = square root of 2x^2+6y^2

Math
Use to rewrite as .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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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 .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Combine fractions.
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Move the negative in front of the fraction.
Combine and .
Move to the denominator using the negative exponent rule .
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Since is constant with respect to , the derivative of with respect to is .
Simplify terms.
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Combine and .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Differentiate using the Power Rule which states that is where .
Combine fractions.
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Combine and .
Multiply by .
Combine and .
Reform the equation by setting the left side equal to the right side.
Replace with .
Find ds/dy s = square root of 2x^2+6y^2


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