Find dy/dx y=(x+7)(x^2-7)

Problem

d()/d(x)*(x+7)*(x2−7)

Solution

1. Identify the function as a product of two binomials, u=x+7 and v=x2−7

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

y=x(x2)+x*(−7)+7*(x2)+7*(−7)

3. Simplify the resulting polynomial.

y=x3−7*x+7*x2−49

4. Reorder the terms by descending powers of x

y=x3+7*x2−7*x−49

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

d(y)/d(x)=d(x3)/d(x)+(d(7)*x2)/d(x)−(d(7)*x)/d(x)−d(49)/d(x)

6. Calculate the derivative of each term.

d(y)/d(x)=3*x2+14*x−7−0

Final Answer

d(y)/d(x)=3*x2+14*x−7

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