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

Differentiate using the Product Rule which states that is where and .
Differentiate.
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.
Rewrite as .
Multiply the exponents in .
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.
Rewrite as .
Multiply the exponents in .
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.
Combine terms.
Combine and .
Move the negative in front of the fraction.
Combine and .
Reorder terms.
Find the Derivative f(y)=(1/(y^2)-9/(y^4))(y+3y^3)