Question

calculus

Answer 1

If y = u^3 and x=5u^2 .
The value of dy/dx at u = 10 is

Answer 2

@mathslover

Answer 3

@iambatman

Answer 4

FInd out

\(\cfrac{dy}{du}\) and \(\cfrac{dx}{du}\)

Divide them, you will get \(\cfrac{dy}{dx}\)/

Answer 5

i have encountered such problem for the first time

Answer 6

dy/dx = 3x^2

Answer 7

Plug in the value of u and you will get your answer.

Actually such type of differentiation is called parametric differentiation.

Answer 8

You must obtain the value of dy/dx in terms of u.

Answer 9

dx/du = 10u

Answer 10

3x^2/10u

3x^2/20

Answer 11

Yeah

Answer 12

Now what is dy/du

Answer 13

I feel like I am now ahead in the Calculus world by learning.

I didn't learn this in AP Calc AB.. But maybe next year in AP Calc BC but now have a clue about so woo head start oh yeah.

Answer 14

Words are missing from my sentence, but you get the idea. No judgement I just woke up.

Answer 15

Never encountered such problem before , thanks @vishweshshrimali5 and @iambatman

Answer 16

answer is 3 actually

Answer 17

:(

Answer 18

Yeah that's correct.

Answer 19

how?

Answer 20

@No.name what is the value of dy/du ?

Answer 21

3x^2/20

Answer 22

Please tell me the value in terms of u only

Answer 23

3x^2/10u

Answer 24

See, its nothing different than dy/dx.

Just ignore that you have x. You only have y in terms of u. I am asking you to differentiate y with respect to u.

Answer 25

I am writing the question again for you:

\(\color{blue}{\text{Originally Posted by}}\) @No.name
If y = u^3
The value of dy/du at u = 10 is
\(\color{blue}{\text{End of Quote}}\)

Answer 26

@No.name can you find out the answer of this question ?

Answer 27

\[\frac{dy}{dx}=\frac{dy}{du} \cdot \frac{du}{dx}\]
finding dy/du is pretty straight forward.
you can find du/dx by first finding dx/du.

Answer 28

@No.name , can you find out dy/du or not ?

Answer 29

3u^2 ?

Answer 30

Yes

Now try finding out dx/du.

Answer 31

10u

Answer 32

Great

Answer 33

Sorry my net is not functioning well , so taking time to reply

Answer 34

Now,

\[\large{\cfrac{dy}{dx} = \cfrac{\cfrac{dy}{du}}{\cfrac{dx}{du}}}\]

Answer 35

Now can you find out dy/dx ?

Answer 36

3u^2/10u

3u/10

Answer 37

Good put u = 10

Answer 38

3

Answer 39

Great there you have it !!

Answer 40

OK I GET IT NOW

Answer 41

THANKS :)

Answer 42

Good job @No.name and nice teaching @vishweshshrimali5 :)

Answer 43

No problem. Enjoy your time with calculus it really is very interesting @No.name

@iambatman that is one of the very few things I am good at :P

Answer 44

One more thing i wanted to ask is what is the derivative of
e^-x

Answer 45

and how do you find it

Answer 46

-e^{-x}

Answer 47

e^(x squared) ?

Answer 48

First find out the derivative of power and then calculate the derivative of the base (here e).

Answer 49

That is use chain rule.

Answer 50

e^(x squared)2x

Answer 51

The same use product rule and then chain rule for each.

Answer 52

Calculus is all about practicing. You should be able to solve calculus problems even while sleeping,

Answer 53

Bye friends :)

Answer 54

Good bye

Answer 55

Wait isn't the derivative of e^-x -e^-x?

Answer 56

Yes it is

Answer 57

Oh okay thought so lol