Question

Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = (x - 3)(x + 3)

Answer 1

Answer:

$f'(x)=2x$

Step-by-step explanation:

Given : Function $f(x)=(x-3)(x+3)$

To find : The derivative of the function by using the Product Rule ?

Solution :

The product rule of derivative is

$\frac{d}{dx}(u\cdot v)=uv'+vu'$

Here, u=x-3 and v=x+3

$\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)\frac{d}{dx}(x+3)+(x+3)\frac{d}{dx}(x-3)$

$\frac{d}{dx}((x-3)\cdot (x+3))=(x-3)1+(x+3)1$

$\frac{d}{dx}((x-3)\cdot (x+3))=x-3+x+3$

$\frac{d}{dx}((x-3)\cdot (x+3))=2x$

Therefore, $f'(x)=2x$

Answer 2

Answer:

$f'(x)=2x$

Step-by-step explanation:

To Find  :Find the derivative of the function by using the Product Rule. Simplify your answer. f(x) = (x - 3)(x + 3)

Solution :

$f(x) = (x - 3)(x + 3)$

We will use chain rule of product

Formula : $uv=u \times v' +v \tyimes u'$

=$(x-3) \times 1+(x+3) \times 1$

=$(x-3)+(x+3)$

=$2x$

So, $f'(x)=2x$

Hence the derivative of the function by using the Product Rule is 2x