Find the Derivative - d/dy 2y^3

Problem

(d(2)*y3)/d(y)

Solution

1. Identify the variable of differentiation, which is y and the function to be differentiated, which is 2*y3

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

(d(2)*y3)/d(y)=2d(y3)/d(y)

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

d(y3)/d(y)=3*y(3−1)

4. Simplify the exponent.

3*y(3−1)=3*y2

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

2⋅3*y2=6*y2

Final Answer

(d(2)*y3)/d(y)=6*y2

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