Find the derivative of $f(x)=(x^3-2)(5x+1)$.

Primary tabs

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

Find the derivative of $f(x)=(x^3-2)(5x+1)$.

Answer: 

$f\,'(x)=20x^3+3x^2-10$

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

We see that $f(x)$ is the product of two functions: $x^3-2$ 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

<Sign in to see all the formulas>

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

<Sign in to see all the formulas>


and

<Sign in to see all the formulas>

Therefore, we know that

<Sign in to see all the formulas>