Question

Can you guys check my answer please and help me as well!! (Derivatives)

Answer 1

and for b i have no idea how to find the derivative when you divide?? please help

Answer 2

we need to know what variable should be differentiate other ways
this a question beyond calc1

Answer 3

you can differentiate with respect to x1
but then you gonna have expressions like \[\frac{d}{dx_1}(x_2)\]

Answer 4

if x_2 x_3 are functions on their own rights

Answer 5

oh okay, ill try to do it right now

Answer 6

so are differentiating \[\frac{d}{dx_1}(y)\] or other variable?

Answer 7

for d/dx_1 would it be 2x_2-2 ?

Answer 8

@xapproachesinfinity we're asked to find the total differential, not the derivative, though the distinction between the concepts can be quite vague and hand-wavy. It is in essence carrying out implicit differentiation on every available variable.

Answer 9

wait so im not doing it right?

Answer 10

No the solution for (a) is correct.

Answer 11

oh didn't read that part of the question actually

Answer 12

thanks for the reminder :)

Answer 13

For part (b), you can use the quotient rule (in addition to the product/chain rules), but perhaps a logarithmic treatment will make things easier to manipulate.
\[\begin{align*}y&=\frac{2x_1x_2-2x_1}{4x_3}\\\\
\ln y&=\ln2+\ln x_1+\ln(x_2-1)-\ln4-\ln x_3\end{align*}\]
Taking the differentials yields
\[\frac{dy}{y}=\frac{dx_1}{x_1}+\frac{dx_2}{x_2-1}-\frac{dx_3}{x_3}\]
Can you take it from here?

Answer 14

yes i will try to do it right now ty!

Answer 15

i like the way you applied logarithm quotient rule without that would be
too much

Answer 16

Okay so would it be : \[(2x_2-2)/x_1+(2x_1)/x_2-(4)/x_3\] ?

Answer 17

wait i meant \[(2x_1)/x_2-1\] for the second one...

Answer 18

\[\begin{align*}\frac{dy}{y}&=\frac{dx_1}{x_1}+\frac{dx_2}{x_2-1}-\frac{dx_3}{x_3}\\\\
dy&=\frac{2x_1x_2-2x_1}{4x_3}\left(\frac{dx_1}{x_1}+\frac{dx_2}{x_2-1}-\frac{dx_3}{x_3}\right)\\\\
&=\frac{x_2-1}{2x_3}\,dx_1+\frac{x_1}{2x_3}\,dx_2-\frac{x_1(x_2-1)}{2{x_3}^2}\,dx_3
\end{align*}\]

Answer 19

Ohhh ok i see i really did it wrong ! Thank you :)