Basic question about chain rule (1 Viewer)

[oompaman]

Hi,

Why can't you use the chain rule for differentiating y=(x+1)^x to find dy/dx?

Thanks

 

[Trebla]

Hi,

Why can't you use the chain rule for differentiating y=(x+1)^x to find dy/dx?

Thanks

Assuming you wrote it correctly, note that a variable is in the index. In standard cases the index is a constant.

 

[oompaman]

then what about something like differentiating y=sin(x^2) is that still chain rule?

Btw the question didn't say to use chain rule, i was just wondering why you couldn't use it.

 

[Trebla]

then what about something like differentiating y=sin(x^2) is that still chain rule?

Yeah. The chain rule is used when you have a function of another function. So in your example x² is a function of x and then you are applying a sine function on top of that function to get sin(x²). Since you have a function of anothe function (also known as a composite function) then you apply the chain rule when differentiating.

 

[funnytomato]

then what about something like differentiating y=sin(x^2) is that still chain rule?

Btw the question didn't say to use chain rule, i was just wondering why you couldn't use it.

yes, it is chain rule, as you can let u=x^2 then d/dx sin(x^2) =d/du sin u * du/dx
or dy/dx= dy/du* du/dx, where y=sin(x^2)

for the 1st question, you can find it if you can find , say d/dx 2^x
if you couldn't differentiate 2^x, think about the definition of log and exponentials (a ^ log_a b = b)

 

[oompaman]

ohhh thanks so much

 

[funnytomato]

actually you do need to apply the chain rule d/dx e^(f(x))= e^(f(x)) * f'(x)