Find dy/dx y=(x+4)(x^2-4)

Problem

d()/d(x)*(x+4)*(x2−4)

Solution

1. Identify the function as a product of two binomials, u=x+4 and v=x2−4

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

y=x(x2)+x*(−4)+4*(x2)+4*(−4)

3. Simplify the resulting polynomial by combining terms.

y=x3+4*x2−4*x−16

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

d(y)/d(x)=d(x3)/d(x)+(d(4)*x2)/d(x)−(d(4)*x)/d(x)−d(16)/d(x)

5. Calculate the derivative of each individual term.

d(y)/d(x)=3*x2+8*x−4−0

Final Answer

d(y)/d(x)=3*x2+8*x−4

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