Find the Derivative - d/dx y=2x^3+6x^2-1

Problem

d()/d(x)*(2*x3+6*x2−1)

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of each term to be taken individually.

d()/d(x)*(2*x3+6*x2−1)=(d(2)*x3)/d(x)+(d(6)*x2)/d(x)−d(1)/d(x)

2. Apply the power rule to the first term, 2*x3 Multiply the exponent by the coefficient and decrease the exponent by one.

(d(2)*x3)/d(x)=6*x2

3. Apply the power rule to the second term, 6*x2 Multiply the exponent by the coefficient and decrease the exponent by one.

(d(6)*x2)/d(x)=12*x

4. Apply the constant rule to the third term, −1 The derivative of any constant is zero.

d(1)/d(x)=0

5. Combine the results to find the final derivative of the expression.

d(y)/d(x)=6*x2+12*x

Final Answer

d()/d(x)*(2*x3+6*x2−1)=6*x2+12*x

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