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frutty [35]
3 years ago
7

Find the derivative of f(x) = 4 divided by x at x = 2.

Mathematics
2 answers:
Natali5045456 [20]3 years ago
8 0

ANSWER

f'(2) = -1

EXPLANATION

The given function is

f(x) =  \frac{4}{x}

Recall that:

\frac{c}{ {a}^{  m} }  = c {a}^{ - m}

We rewrite the given function using this rule to obtain,

f(x) =  4 {x}^{ - 1}

Recall again that,

If

f(x)= a {x}^{n}

then

f'(x)=n a {x}^{n - 1}

We differentiate using the power rule to obtain,

f'(x) = - 1 \times  4 {x}^{ - 1 - 1}

f'(x) =  -  4 {x}^{ - 2}

We rewrite as positive index to obtain,

f'(x) = -  \frac{4}{ {x}^{2} }

We plug in x=2 to obtain,

f'(2) = -  \frac{4}{ { (2)}^{2} }  =  -  \frac{4}{4}  =  - 1

polet [3.4K]3 years ago
4 0
<h2>Hello!</h2>

The answer is:

f'(2)=-1

<h2>Why?</h2>

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

f(x)=\frac{4}{x}

It's a quotient, so, we need to use the following formula to derivate it:

f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }

Then, of the given function we have that:

u=4\\v=x

So, derivating we have:

f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }

f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }

f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }

f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }

Hence,

f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }

Now, evaluating with x equal to 2, we have:

f'(2)=\frac{-4}{(2)^{2} }

f'(2)=\frac{-4}{4}

f'(2)=-1

Therefore, the answer is:

f'(2)=-1

Have a nice day!

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