Find the Derivative - d/dx x(11-2x)(19-2x)

Problem

d()/d(x)*x*(11−2*x)*(19−2*x)

Solution

1. Expand the expression by multiplying the two binomials first.

(11−2*x)*(19−2*x)=209−22*x−38*x+4*x^2

=4*x^2−60*x+209

2. Distribute the x into the resulting quadratic expression to obtain a polynomial.

x*(4*x^2−60*x+209)=4*x^3−60*x^2+209*x

3. Apply the power rule d()/d(x)*x^n=n*x^(n−1) to each term of the polynomial.

(d(4)*x^3)/d(x)=12*x^2

(d(−)*60*x^2)/d(x)=−120*x

(d(209)*x)/d(x)=209

4. Combine the results to find the final derivative.

d()/d(x)*(4*x^3−60*x^2+209*x)=12*x^2−120*x+209

Final Answer

d()/d(x)*x*(11−2*x)*(19−2*x)=12*x^2−120*x+209

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