Question

why is (x+deltax)^2 =x^2+2xdeltax+ deltax^2? Trying to find derivative of f(x)+ x^2 +(0.01)x +5

Answer 1

\(\large\color{slate}{ (a+b)^2=a^2+2ab+b^2 }\)

Answer 2

In your case:

\(\large\color{slate}{ a=x }\)
\(\large\color{slate}{ b=\Delta x }\)

Answer 3

I see no purpose in this expression as far as actual problem goes, but...

Answer 4

That makes sense!! Thanks! Trying to relearn calc 1 in prep for calc 2

Answer 5

oh I didn't read the second sentence

Answer 6

i don't know why people get confused when they see that delta hehe

Answer 7

you are trying to differentiate? I think there is likely more to this problem then...

Answer 8

I mean more info

Answer 9

and you mean `f(x)=` , or `f(x)+ ` ?

Answer 10

f(x)=

Answer 11

oh, I thought it is one of those limits, like Reinnmun sum formulas that you have incorrectly written...

\(\large\color{slate}{ f(x)= x^2 +(0.01)x +5 }\)

then you can find \(\large\color{slate}{ f'(x) }\) using simple rules.

Answer 12

but if you are differentiating the function, \(\large\color{slate}{ f(x)= x^2 +(0.01)x +5 }\)
then what does \(\large\color{slate}{ (x+\Delta x)^2 }\) have to do with anything ?

Answer 13

I was just trying to simplify to find the derivative

Answer 14

anyways, you just need to find the derivative of, \(\large\color{slate}{ f'(x)= x^2 +(0.01)x +5}\)

Answer 15

I mean the derivative of \(\large\color{slate}{ f(x)= x^2 +(0.01)x +5}\) , excuse me

Answer 16

apply the power rule to \(\large\color{slate}{ x^2 }\) what do you get

Answer 17

?

Answer 18

\(\large\color{black}{ \frac{\LARGE d}{\LARGE dx}\left(\begin{matrix} x^n\\ \end{matrix}\right) =n\cdot x^{n-1} }\)

Answer 19

(d/dx is a notation for derivative)
so applying this rule, (known as the "power rule")

can you finish the following?

\(\large\color{black}{ \frac{\LARGE d}{\LARGE dx}\left(\begin{matrix} x^2\\ \end{matrix}\right) = }\)

Answer 20

Im lost now

Answer 21

do you know the power rule for the derivative?

Answer 22

I dont remember