Find the derivative of f(x)=(x3−2)(5x+1).

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Lesson Parent: 
Differentiation IV: Differentiation Formulas Everyone Must Know
Problem: 

Find the derivative of f(x)=(x3−2)(5x+1).

Answer: 

f′(x)=20x3+3x2−10

SAMPLE SOLUTION

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Solution: 

We see that f(x) is the product of two functions: x3−2 and 5x+1. In this case we should use the Product Rule. Let's call <Sign in to see all the formulas> and <Sign in to see all the formulas>. Now <Sign in to see all the formulas> and the Product Rule says that

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Because both h(x) and g(x) are polynomials and we know the derivative of a polynomial, then we know that

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and

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Therefore, we know that

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