MX1 Question (1 Viewer)

[scaryshark09]

Just had exam and this was a question (something like this)

y = 2x(x+3)^6

find the derivative of the inverse function in terms of y.

Does anyone know how to solve it?

 

[cossine]

Definition of inverse function: So if (x, y) is a point of function f, then (y, x) is a point of f^-1.

According to the definition we swap the coordinates since (x, y) is swapped so it becomes (y, x)
=> x = 2y(y+3)^6

From there take the derivative on both sides using implicit differentiation for the RHS.

 

[scaryshark09]

what is implicit differentiation?
is that the same as the product rule?

 

[scaryshark09]

what is the actual answer cause some peeople got

2(7y+6)(x+6)^6
and some got 1/(this answer)

the question was actually y = 2x(x+6)^2

 

[scaryshark09]

once you differentiate, do you do 1 over the answer???
some people said you do because otherwise it's dx/dy not dy/dx

 

[carrotsss]

what is the actual answer cause some peeople got

2(7y+6)(x+6)^6
and some got 1/(this answer)

the question was actually y = 2x(x+6)^2

That’s it if that’s the question

 

[cossine]

what is implicit differentiation?
is that the same as the product rule?

Basically when you differentiate y you just add dy/dx. This comes from the chain rules since.

d f(y)/dx = dy/dx * df(y)/dy

E.g., d/dx y^2 = 2y*dy/dx

carrotsss is another way to do it without using implicit differentiation.