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zhenek [66]
3 years ago
6

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

Mathematics
2 answers:
Minchanka [31]3 years ago
8 0

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

Morgarella [4.7K]3 years ago
3 0

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

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