Find the Derivative - d/dx y=3x-1

Problem

d()/d(x)*(3*x−1)

Solution

1. Identify the expression to be differentiated, which is a linear function of the form ƒ(x)=3*x−1

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(3*x−1)=(d(3)*x)/d(x)−d(1)/d(x)

3. Apply the constant multiple rule to the first term, (d(3)*x)/d(x)=3d(x)/d(x)

4. Apply the power rule to d(x)/d(x) which results in 1

(d(3)*x)/d(x)=3*(1)=3

5. Apply the constant rule to the second term, noting that the derivative of any constant is 0

d(1)/d(x)=0

6. Combine the results to find the final derivative.

3−0=3

Final Answer

d()/d(x)*(3*x−1)=3

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