Find the Derivative - d/dx ax^2+bx+c

Problem

d()/d(x)*(a*x2+b*x+c)

Solution

1. Apply the sum rule for differentiation, which allows us to take the derivative of each term individually.

(d(a)*x2)/d(x)+(d(b)*x)/d(x)+d(c)/d(x)

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

(d(a)*x2)/d(x)=2*a*x

3. Apply the power rule to the second term, treating b as a constant.

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

4. Apply the constant rule to the third term, noting that the derivative of any constant c is zero.

d(c)/d(x)=0

5. Combine the results to find the final derivative.

2*a*x+b+0

Final Answer

(d(a)*x2+b*x+c)/d(x)=2*a*x+b

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