Find the Derivative - d/dx 3x^2-2x

Problem

d()/d(x)*(3*x2−2*x)

Solution

1. Apply the sum/difference rule of differentiation, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(3*x2−2*x)=(d(3)*x2)/d(x)−(d(2)*x)/d(x)

2. Apply the constant multiple rule to pull the constants out of the derivatives.

(d(3)*x2)/d(x)−(d(2)*x)/d(x)=3d(x2)/d(x)−2d(x)/d(x)

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

3*(2*x(2−1))−2*(1*x(1−1))

4. Simplify the expression by performing the multiplication and handling the exponents.

6*x−2

Final Answer

d()/d(x)*(3*x2−2*x)=6*x−2

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