Implicit differentiation: how to tell when to use, when not?

[masterbsk]

I've just learned about implicit differentiation, and I'm a little confused. The format in which a question is solved for implicit is no different than what I have been doing up 'till now (derivative). So how do I tell apart when to use implicit, and when not to? (how do I know when to use the dy^n/dy x dy/dx = n x (y^n-1) x (y') formula for implicit, and when not to?)

Is it an implicit question if the formula dy/dx is included in the sentence?

 

[Deleted member 4993]

Re: Implicit differentiation

I've just learned about implicit differentiation, and I'm a little confused. The format in which a question is solved for implicit is no different than what I have been doing up 'till now (derivative). So how do I tell apart when to use implicit, and when not to? (how do I know when to use the dy^n/dy x dy/dx = n x (y^n-1) x (y') formula for implicit, and when not to?)

Is it an implicit question if the formula dy/dx is included in the sentence?

You can ALWAYS use implicit differentiation

for example if you have the following equation:

xy = C

using implicit differentiation

y + xy' = 0

y' = - y/x = - xy/x[sup:3i2vpeyf]2[/sup:3i2vpeyf] = - C/x[sup:3i2vpeyf]2[/sup:3i2vpeyf]

using non-implicit differentiation:

xy = C

y = C/x

y' = -C/x[sup:3i2vpeyf]2[/sup:3i2vpeyf]

and those give you the same answer (as those should).

We have to use implicit differentiation when we cannot write the function as y = f(x)

suppose you have an expression as:

x + ln(x) + sin(x) = y + ln(y) + cos(y)

In this case, you have to use implicit differentiation - because there is no-way you can write it as y = f(x).

 

[masterbsk]

Oh, ok. Thank you. Now I understand.

One thing though, I don't understand how xy = C => y + xy' = 0 through implicit.

 

[galactus]

Oh, ok. Thank you. Now I understand.

One thing though, I don't understand how xy = C => y + xy' = 0 through implicit.

It's the product rule.

 

[masterbsk]

Oh, ok. Thank you. Now I understand.

One thing though, I don't understand how xy = C => y + xy' = 0 through implicit.

It's the product rule.

Ohhhh. Fail. Thanks.