Find the Derivative - d/dx 4x^3-88x^2+484x

Problem

d()/d(x)*(4*x3−88*x2+484*x)

Solution

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

(d(4)*x3)/d(x)−(d(88)*x2)/d(x)+(d(484)*x)/d(x)

2. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term, multiplying the exponent by the coefficient and decreasing the exponent by one.

4*(3*x2)−88*(2*x)+484*(1)

3. Simplify the expression by performing the multiplication for each term.

12*x2−176*x+484

Final Answer

d()/d(x)*(4*x3−88*x2+484*x)=12*x2−176*x+484

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