Find the Derivative - d/dx [(x^2+x^3)(x+9)]

Problem

d()/d(x)*[(x2+x3)*(x+9)]

Solution

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

(x2+x3)*(x+9)=x3+9*x2+x4+9*x3

2. Combine like terms to write the polynomial in standard form.

x4+10*x3+9*x2

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

d(x4)/d(x)=4*x3

(d(10)*x3)/d(x)=30*x2

(d(9)*x2)/d(x)=18*x

4. Sum the resulting derivatives to find the final expression.

4*x3+30*x2+18*x

Final Answer

d()/d(x)*[(x2+x3)*(x+9)]=4*x3+30*x2+18*x

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