Question

Guys, kindly help.. calculus
Find d/dx(2y/5x)

Answer 1

@Flava Hi,

\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

since you are differentiating with respect to x, y will be treated as constant(unless y is the function of x)
so you can pull that out , giving (2y/5) d/dx (1/x)
can u differentiate 1/x ?

Answer 2

not sure, im still green in this. what's the answer

Answer 3

1/x can be written as x^(-1)
and differentiation of x^n is n x^{n-1}
now can u differentiate x^(-1) ??
juat put n=-1 in the formula.

Answer 4

*just

Answer 5

@Flava we do not just give answers here, please read http://openstudy.com/code-of-conduct

Answer 6

im working it out, sorry you were too fast.
I actually want to understand not just the answer,

Answer 7

that is good. I will wait till you calculate d/dx (1/x)

Answer 8

d/dx(1/x) = x^-1
how do you proceed from here

Answer 9

thats not correct.
1/x = x^(-1)
d/dx(1/x) = d/dx(x^(-1)) = ??

Answer 10

=-x^2

Answer 11

it will be -x^(-2)
so d/dx (2y/5x) = 2y/5 * (-x^(-2))
or
-2y/5x^2
ok?

Answer 12

thanks so much, highly appreciated

Answer 13

welcome ^_^

Answer 14

hartnn - can we try another one... if 3x^2+2x^2y^3-5/4y^2=0, evaluate dy/dx when x=1/2 and y=1

dy/dx = 6x+4x3y^2-5y-2 then substiute x..?

Answer 15

@Flava that last question uses implicit differentiation, once done then plug the values of x and y
implicit differentiation is different to normal differentiation

Answer 16

thanks for advis pls help, im not good on implict diff'. I understand the normal differentiation

Answer 17

@Flava to tell you the truth I can solve it, but I find explaining implicit is very difficult, when you study it you will know what I mean, maybe @amistre64 or @UnkleRhaukus can help explaining it, or guide you elsewhere

Answer 18

ok, how do you solve it. When i see the workings i will be able to see the difference from the normal differenciation

Answer 19

\[\qquad\qquad\qquad3x^2+2x^2y^3-\frac54y^2=0\]\[6x+4xy^3+6x^2y^2\frac{\text dy}{\text dx}-\frac52y\frac{\text dy}{\text dx}=0\]

Answer 20

thanks Unkle

Answer 21

\[6x+4xy^3+\left(6x^2y^2-\frac52y\right)\frac{\text dy}{\text dx}=0\]
\[6x+4xy^3=\left(\frac52y-6x^2y^2\right)\frac{\text dy}{\text dx}\]
\[\frac{\text dy}{\text dx}=\frac{6x+4xy^3}{\left(\frac52y-6x^2y^2\right)}\]

Answer 22

now sub in \((1/2,1)\)

Answer 23

the confusion and difficulty difference between explicit and implicit differentation stems from the way that a derivative is taught to begin with. We are simply not taught how vital the chain rule is to begin with.

Answer 24

if we allow x and y to be functions of some unknown variable then we simply apply the chain rule.

for example,

D[4x^3] = 3*4x^2 * (x')

it is only in using the information that the derivative is with respect to "x" that we can then simplify this to x' = 1

Answer 25

maybe Leibniz's notation is the most transparent here

Answer 26

i agree; if we chain out a dx/dx its quite obvious what the behind the scenes workings are

Answer 27

Unckle

Thanks I was offline a bit. Aftr substituting I have got 5 as the answer

Amsistre64 - i agree with you,most lecturers do not give clear disptinction between the two differentiation hence confising us

Answer 28

Hartnn / Uncle
kindly check for me if I've done this right...

Find the gradient of the tangent drawn to the circle x^2+y^2=16 at the point where x=2 (current to 4s.f)
My Soln:
d/dx[x^2+y(x)^2=2x+2ydy/dx=0
2ydy/dx=-2x
dy/dx = -x/y
at x=2
-2/y

Answer 29

five is good fot the first question

Answer 30

Uncle - thanks, what of the 2nd one

Answer 31

your working looks fine

Answer 32

there should be tow solutions right?

Answer 33

what's the other soln?