Find the Derivative - d/dx (x+3)(x^2-3)

Problem

d()/d(x)*(x+3)*(x2−3)

Solution

1. Identify the expression as a product of two functions, u=x+3 and v=x2−3 which suggests using the product rule.

2. Apply the product rule formula, which states that d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x)

3. Calculate the derivatives of the individual parts: d(x+3)/d(x)=1 and d(x2−3)/d(x)=2*x

4. Substitute these values into the product rule formula.

d()/d(x)*(x+3)*(x2−3)=(x+3)*(2*x)+(x2−3)*(1)

5. Distribute the terms to expand the expression.

(x+3)*(2*x)+(x2−3)=2*x2+6*x+x2−3

6. Combine like terms to reach the final simplified form.

2*x2+x2+6*x−3=3*x2+6*x−3

Final Answer

d()/d(x)*(x+3)*(x2−3)=3*x2+6*x−3

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