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

Problem

d()/d(x)*(3*x2−5*x)

Solution

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

d()/d(x)*(3*x2−5*x)=(d(3)*x2)/d(x)−(d(5)*x)/d(x)

2. Apply the constant multiple rule to move the coefficients outside of the derivatives.

3d(x2)/d(x)−5d(x)/d(x)

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

3*(2*x)−5*(1)

4. Simplify the resulting expression by performing the multiplication.

6*x−5

Final Answer

d()/d(x)*(3*x2−5*x)=6*x−5

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