Find dy/dx y=(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)

y=x3−9*x+9*x2−81

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

y=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(y)/d(x)=d(x3)/d(x)+(d(9)*x2)/d(x)−(d(9)*x)/d(x)−d(81)/d(x)

4. Calculate the derivative of each term.

d(y)/d(x)=3*x2+18*x−9−0

Final Answer

d(y)/d(x)=3*x2+18*x−9

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