Find the Derivative - d/dx y=3x-7 , y<-4x-5

Problem

d()/d(x)*(3*x−7)

Solution

1. Identify the function to be differentiated, which is y=3*x−7

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually: d()/d(x)*(3*x−7)=(d(3)*x)/d(x)−d(7)/d(x)

3. Apply the power rule to the first term, where (d(a)*x)/d(x)=a Thus, (d(3)*x)/d(x)=3

4. Apply the constant rule to the second term, where the derivative of any constant is zero. Thus, d(7)/d(x)=0

5. Combine the results to find the final derivative. Note that the inequality y<−4*x−5 defines a region but does not change the differentiation process of the specific linear function y=3*x−7

Final Answer

d(y)/d(x)=3

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