Find the Derivative - d/dx f(x)=mx+b

Problem

d()/d(x)*(m*x+b)

Solution

1. Identify the function as a linear expression where m and b are constants.

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

d()/d(x)*(m*x+b)=(d(m)*x)/d(x)+d(b)/d(x)

3. Apply the constant multiple rule to the first term, moving the constant m outside the derivative.

(d(m)*x)/d(x)=md(x)/d(x)

4. Evaluate the derivative of x with respect to x which is 1

m(1)=m

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

d(b)/d(x)=0

6. Combine the results to find the final derivative.

m+0=m

Final Answer

d()/d(x)*(m*x+b)=m

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