Find the Derivative - d/dx y=-2x+5

Problem

d()/d(x)*(−2*x+5)

Solution

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

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

d()/d(x)*(−2*x+5)=(d(−)*2*x)/d(x)+d(5)/d(x)

3. Apply the constant multiple rule to the first term, pulling the constant −2 out of the derivative.

(d(−)*2*x)/d(x)=−2d(x)/d(x)

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

−2*(1)=−2

5. Evaluate the derivative of the constant 5 which is 0

d(5)/d(x)=0

6. Combine the results to find the final derivative.

−2+0=−2

Final Answer

d()/d(x)*(−2*x+5)=−2

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