Question

differentiate

Answer 1

do you know product rule and chain rule ?

Answer 2

i know product rule..chain rule i understand a little

Answer 3

ok, so give it a shot, use product rule to differentiate :
x^4y^5
what u get ?

Answer 4

4x^3*y^5+x^4*5y^4

Answer 5

when you differentiate any function of 'y' , with respect to 'x' , like say f(y), you use chain rule and get f'(y) dy/dx

similarly when you differentiated y^5 here, you would get 5y^4 dy/dx
got this ?

Answer 6

yeah so did i do the above correctly?

Answer 7

just multiply the last term by dy/dx
everything else is correct

Answer 8

why the last term? 5y^4?

Answer 9

\(4x^3y^5+x^4 5y^4D\)
that should go into your result box :)

Answer 10

yes,
because you differentiated the function of y aka y^5 only in 2nd term, so dy/dx will be multiplied only in 2nd term

Answer 11

\(4x^3y^5+5x^4 y^4D\)

Answer 12

okay i kind of understand it

Answer 13

if you practice a few more problems you will get it clearly :)
as its not difficult at all.

Answer 14

oh okay but it says to respect to x...why are we focusing on y?

Answer 15

since we r diff w.r.t x, thats why we need chain rule for differentiating a function of 'y' !
else if we differentiate a function of 'x' say x^9, we won't need chain rule, it'll be just 9x^8
but for y^9, differentiating w.r.t x would give 9y^8 dy/dx

Answer 16

okay hmm im not clearly understanding it but i will eventually! thanks again!! :)

Answer 17

similarly if we differentiate x^9 w.r.t y , we would get 9x^8 dx/dy
ok, welcome ^_^

Answer 18

@hartnn im having a problem with another example

Answer 19

sure, ask :)

Answer 20

(x^2+y^2)^7

Answer 21

i did what you told me but its not working

Answer 22

whats your answer ?

Answer 23

i got 7(x^2+y^2)^6*2x*Dy^2+2y*x^2

Answer 24

is the answer close? or very far lol

Answer 25

7(x^2+y^2)^6 part is correct ....

Answer 26

the second part is g'(x)

Answer 27

then
d/dx (x^2+y^2) = (2x +2y D)

Answer 28

thats it!

Answer 29

what happend to the other part?

Answer 30

i mean
7(x^2+y^2)^6 (2x +2y D)

Answer 31

oh okay i think i differtiated that part wrong

Answer 32

yeah, diff of x^2 is just 2x
and y^2 is just 2ydy/dx