Find dy/dx y=x^3+6x^2

Problem

d()/d(x)*(x^3+6*x^2)

Solution

1. Identify the function to be differentiated, which is y=x^3+6*x^2

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

3. Apply the power rule to each term, where d(x^n)/d(x)=n*x^(n−1)

4. Differentiate the first term x^3 to get 3*x^2

5. Differentiate the second term 6*x^2 by multiplying the constant by the exponent to get 12*x

6. Combine the results to find the final derivative.

Final Answer

d(y)/d(x)=3*x^2+12*x

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