Find the Derivative - d/dy 2y^3

Problem

(d(2)*y^3)/d(y)

Solution

1. Identify the variable of differentiation, which is y and the function to be differentiated, which is 2*y^3

2. Apply the constant multiple rule by moving the constant 2 outside of the derivative.

(d(2)*y^3)/d(y)=2d(y^3)/d(y)

3. Apply the power rule, which states that d(y^n)/d(y)=n*y^(n−1)

d(y^3)/d(y)=3*y^(3−1)

4. Simplify the exponent.

3*y^(3−1)=3*y^2

5. Multiply the result by the constant 2 to find the final derivative.

2⋅3*y^2=6*y^2

Final Answer

(d(2)*y^3)/d(y)=6*y^2

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