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

Problem

d()/d(x)*(x+9)*(x2−9)

Solution

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

(x+9)*(x2−9)=x(x2)+x*(−9)+9*(x2)+9*(−9)

=x3−9*x+9*x2−81

2. Rearrange the terms in descending order of their powers.

x3+9*x2−9*x−81

3. Apply the power rule to each term individually, where d(xn)/d(x)=n*x(n−1)

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

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

(d(−)*9*x)/d(x)=−9

(d(−)*81)/d(x)=0

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

3*x2+18*x−9

Final Answer

d()/d(x)*(x+9)*(x2−9)=3*x2+18*x−9

Want more problems? Check here!