Find the Derivative - d/d@VAR f(x)=(x^2+2x)(x+1)

Problem

d()/d(x)*(x2+2*x)*(x+1)

Solution

1. Identify the function as a product of two binomials, u(x)=x2+2*x and v(x)=x+1

2. Expand the expression using the FOIL method to simplify the differentiation process.

ƒ(x)=x(x)2+x(1)2+2*x(x)+2*x(1)

3. Combine like terms to rewrite the function in standard polynomial form.

ƒ(x)=x3+x2+2*x2+2*x

ƒ(x)=x3+3*x2+2*x

4. Apply the power rule, which states d(xn)/d(x)=n*x(n−1) to each term of the polynomial.

d(x3)/d(x)=3*x2

(d(3)*x2)/d(x)=6*x

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

5. Sum the resulting derivatives to find the final derivative of the function.

d(ƒ)/d(x)=3*x2+6*x+2

Final Answer

d()/d(x)*(x2+2*x)*(x+1)=3*x2+6*x+2

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