Find the Derivative - d/d@VAR f(x)=-3x^2+6x-8

Problem

d()/d(x)*(−3*x2+6*x−8)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term in the polynomial individually.

d()/d(x)*(−3*x2+6*x−8)=(d(−)*3*x2)/d(x)+(d(6)*x)/d(x)−d(8)/d(x)

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

(d(−)*3*x2)/d(x)=−3*(2)*x(2−1)=−6*x

3. Apply the power rule to the second term, noting that x is x1

(d(6)*x)/d(x)=6*(1)*x(1−1)=6

4. Apply the constant rule to the third term, as the derivative of any constant is zero.

d(8)/d(x)=0

5. Combine the results to find the final derivative of the function.

−6*x+6−0=−6*x+6

Final Answer

d()/d(x)*(−3*x2+6*x−8)=−6*x+6

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