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

Problem

d()/d(x)*(x3−3/2*x2)

Solution

1. Identify the expression as a difference of two terms and apply the sum/difference rule for differentiation.

d()/d(x)*(x3−3/2*x2)=d(x3)/d(x)−d()/d(x)3/2*x2

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

d(x3)/d(x)=3*x2

3. Apply the constant multiple rule and the power rule to the second term.

d()/d(x)3/2*x2=3/2⋅2*x

4. Simplify the resulting expression by multiplying the constants.

3/2⋅2*x=3*x

5. Combine the results of the derivatives.

3*x2−3*x

Final Answer

d()/d(x)*(x3−3/2*x2)=3*x2−3*x

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