Question

Last one guys, Sorry!

Can someone show me how to do this step by step!?

Use implicit differentiation to find dy/dx
cos(xy)=x

Answer 1

use chain rule

Answer 2

-sin(x*y)* ( 1* y + x * y ' ) = 1

Answer 3

\[\frac{d}{dx}\cos(w) = \frac{d}{dx}(\cos(w)) \times \frac{d}{dx}(w) = -\sin(w) \cdot \frac{d}{dx}(w)\]

Answer 4

First we take derivative of function, which is cos here and then we take derivative of its angle.. :)

Answer 5

you have a mistake

Answer 6

d/dx cos (w) = d/dw (cos(w)) * d/dx (w)

Answer 7

d/dw (cos(w)) = - sin(w)

Answer 8

I am getting you.. :) thanks for informing that.. :)

Answer 9

Oh fine point.

Answer 10

So do we have to simplify your answer perl?

Answer 11

we can distribute

Answer 12

or is that the final product?

Answer 13

since you want to solve for y ' , which is dy/dx

Answer 14

right.

Answer 15

I think he has missed \(y\) there ? Right?

Answer 16

\(-\sin(xy)[1 \cdot y + x \cdot y'] = 1\)
\(-\color{red}{y} \sin(xy) - xy' \sin(xy) = 1 \)

Answer 17

yes, woops

Answer 18

this 'live preview' is forcing me to see double, which is distracting

Answer 19

take \(-y \sin(xy)\) to other side :

\[-x \cdot y' \sin(xy) = 1 + y \sin(xy) \implies y' = ??\]

Answer 20

cos(x*y) = 1

implicit derivative:

-sin(x*y)* ( 1* y + x * y ' ) = 1

- sin(xy) * y - sin(xy) * x * y ' = 1

- sin(xy) *x * y ' = 1 + y * sin(xy)

y ' = ( 1 + y * sin (xy ) ) / (- x* sin xy)

Answer 21

Oh no worries! Okay awesome! Thank you all sooo much for all your help! You're lifesavers!! :) I wish I could give you all a million metals lol Have a great night!