Question

how to find dw/dx of w= x+4

Answer 1

Just take the derivative with respect to x,

Answer 2

HOw?

Answer 3

the answer is 1 but i cant understand how?

Answer 4

\[w=x+4\]\[\frac{dw}{dx} = \frac{dx}{dx}+\frac{d4}{dx}\]This is just like taking the derivative. Have you learned how to take derivatives?

Answer 5

no

Answer 6

Because w is a FUNCTION of x, when we're taking the derivative of a variable with respect to another variable, we label that as a prime, \(w'\). If we're taking the derivative of a variable with respect to itself, it depends upon the power rule of the variable. in this case, \(\frac{d}{dx}(x^1) = 1\)

Answer 7

These are just rules in your Calculus book you have to follow. http://www.mathsisfun.com/calculus/derivatives-introduction.html use this for more information about finding derivatives.

Answer 8

@Ghayyas.mubashir Do you know the definition of a derivative?

Answer 9

Have you seen this: \[
\frac{df}{dx} = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}
\]

Answer 10

yeh but i cant understand that

Answer 11

Okay, let's start from the basics then...

Answer 12

yes plzz

Answer 13

\[
w = f(x) = x+4
\]Do you understand this?

Answer 14

yeh

Answer 15

Okay, now: \[
f(\color{red}{x+h}) = (\color{red}{x+h})+4
\]Does this make sense?

Answer 16

We substituted in \(x+h\) for \(x\).

Answer 17

yeh

Answer 18

Now we plug these into the limit. \[
\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to 0}\frac{(x+h+4)-(x+4)}{h}
\]

Answer 19

Do you understand the substitutions I did here?

Answer 20

yes

Answer 21

Can you simplify: \[
\lim_{h\to 0}\frac{(x+h+4)-(x+4)}{h}
\]?

Answer 22

wait a min i try

Answer 23

i cant

Answer 24

\[
\lim_{h\to 0}\frac{(x+h+4)-(x+4)}{h} =
\lim_{h\to 0}\frac{x+h+4-x-4}{h} =\lim_{h\to 0}\frac{h}{h}=\lim_{h\to0}1=1
\]?

Answer 25

\[
\frac{dw}{dx}=\frac{df}{dx}=1
\]

Answer 26

May god help you if you ever are tested on this.

Answer 27

h/h =0 then y is equal to 1?

Answer 28

???

Answer 29

You make me sad.

Answer 30

soory but plz if u can

Answer 31

\[
\frac 44 = ?
\]

Answer 32

1

Answer 33

\[
\frac hh = ?
\]

Answer 34

but h = 0

Answer 35

0/0 ? = 1?

Answer 36

No, that isn't how limits work.

Answer 37

any number that has limit 0 it would be always one??

Answer 38

When you are doing a limit, like \[
\lim_{x\to a}f(x)
\]Then you assume that \(x\) is very close to \(a\), but that \(x\neq a\).

Answer 39

hey ghayyas

Answer 40

You should really use the link I provided you in the posts above to learn about limits and derivatives to get a general idea of how they work.

Answer 41

you are learning first principle?

Answer 42

first principle is basically comes from the equation of a line

Answer 43

hi dan815 abd thank you much jhanny bean and best regards wio

Answer 44

dian i understand now. thank you so much

Answer 45

okay

Answer 46

np

Answer 47

a big thans to wio who help me alot.. Thank you SOOOOO MUCH,,

Answer 48

You're welcome.


"First principle"
Where does that even come from?

Answer 49

Is there a second principle?

Answer 50

what is first principle>?

Answer 51

Yeah that's what i'm wondering.