Find the Derivative f(y)=(1/(y^2)-3/(y^4))(y+9y^3)

Math
Differentiate using the Product Rule which states that is where and .
Differentiate.
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By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
By the Sum Rule, the derivative of with respect to is .
Apply basic rules of exponents.
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Rewrite as .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply by .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Apply basic rules of exponents.
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Rewrite as .
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply by .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite the expression using the negative exponent rule .
Rewrite the expression using the negative exponent rule .
Simplify.
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Combine terms.
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Combine and .
Move the negative in front of the fraction.
Combine and .
Reorder terms.
Find the Derivative f(y)=(1/(y^2)-3/(y^4))(y+9y^3)

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