Differentiate using the Product Rule which states that is where and .

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 .

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)