Question

Derivative of f(x)=5.2x+2.3​

Answer 1

Answer:

5.2

Step-by-step 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, $\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$.

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:

$\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

$\lim_{h \rightarrow 0} \frac{[5.2(x+h)+2.3]-[5.2x+2.3]}{h}$

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].

$\lim_{h \rightarrow 0} \frac{5.2x+5.2h+2.3-5.2x-2.3}{h}$

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.

$\lim_{h \rightarrow 0} \frac{5.2h}{h}$

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

$\lim_{h \rightarrow 0}5.2$

5.2

Answer 2

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