Find dy/dx y=(x+3)(x^2-3)

Problem

d()/d(x)*(x+3)*(x2−3)

Solution

1. Identify the function as a product of two binomials, u=x+3 and v=x2−3

2. Apply the product rule for differentiation, which states d(y)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: d(x+3)/d(x)=1 and d(x2−3)/d(x)=2*x

4. Substitute these derivatives back into the product rule formula:

d(y)/d(x)=(x+3)*(2*x)+(x2−3)*(1)

5. Distribute the terms to simplify the expression:

d(y)/d(x)=2*x2+6*x+x2−3

6. Combine like terms to find the final derivative:

d(y)/d(x)=3*x2+6*x−3

Final Answer

d(y)/d(x)=3*x2+6*x−3

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