Question

Derivative of f(x)=5.2x+2.3​

Answer 1

`f(x)=5.2x+2.3\\f'(x)=5.2`

Answer 2

5.2

Explanation:

Since you have a linear function, asking for derivative is equivalent to asking for the slope.

The slope of y=5.2x+2.3 is 5.2 so the derivative is 5.2 .

However, if you really want to use the definition of derivative, you may.

That is,
`\lim_(h \rightarrow 0) (f(x+h)-f(x))/(h)`.

We know
`f(x)=5.2x+2.3` so
`f(x+h)=5.2(x+h)+2.3`. All I did was replace any x in the 5.2x+2.3 with (x+h) to obtain f(x+h).

Let's plug it into our definition:

`\lim_(h \rightarrow 0) (f(x+h)-f(x))/(h)`

`\lim_(h \rightarrow 0) ([5.2(x+h)+2.3]-[5.2x+2.3])/(h)`

Now we need to do some distributing. I see I need this distributive property both for the 5.2(x+h) and the -[5.2x+2.3].

`\lim_(h \rightarrow 0) (5.2x+5.2h+2.3-5.2x-2.3)/(h)`

There are some like terms to combine in the numerator. The cool thing is they are opposites and when you add opposites you get 0.

`\lim_(h \rightarrow 0) (5.2h)/(h)`

There is a common factor in the numerator and denominator. h/h=1.

`\lim_(h \rightarrow 0)5.2`

5.2