Find the Derivative - d/d@VAR f(x)=-3x^2-36x-19

Problem

d()/d(x)*(−3*x2−36*x−19)

Solution

1. Identify the function to be differentiated, which is a polynomial ƒ(x)=−3*x2−36*x−19

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

3. Apply the power rule to the first term, where (d(a)*xn)/d(x)=a*n*x(n−1)

(d(−)*3*x2)/d(x)=−6*x

4. Apply the power rule to the second term.

(d(−)*36*x)/d(x)=−36

5. Apply the constant rule to the third term, noting that the derivative of a constant is zero.

(d(−)*19)/d(x)=0

6. Combine the results of the individual derivatives to find the final expression.

Final Answer

(d(−)*3*x2−36*x−19)/d(x)=−6*x−36

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