Find the Derivative - d/dx 5x^2-x^3

Problem

d()/d(x)*(5*x2−x3)

Solution

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

d()/d(x)*(5*x2−x3)=(d(5)*x2)/d(x)−d(x3)/d(x)

2. Apply the constant multiple rule to the first term by moving the coefficient outside of the derivative.

(d(5)*x2)/d(x)=5⋅d(x2)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to both terms.

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

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

4. Multiply and simplify the resulting expressions to find the final derivative.

5*(2*x)−3*x2=10*x−3*x2

Final Answer

d()/d(x)*(5*x2−x3)=10*x−3*x2

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