Confused derivative

[Loki123]

How do I get RHS from LHS?

 

[R.M.]

I think you are getting hung up on notation. I interpret the left hand side as "the derivative of the function P(t)". I interpret the right hand side as "P prime of t with respect to t".

 

[Loki123]

I think you are getting hung up on notation. I interpret the left hand side as "the derivative of the function P(t)". I interpret the right hand side as "P prime of t with respect to t".

Could you define the RHS a bit more in detail? I am having trouble understanding it.

 

[BigBeachBanana]

Could you define the RHS a bit more in detail? I am having trouble understanding it.

[math]\frac{d(\phi(t))}{dt}=\phi'(t)\\ d(\phi(t))=\phi'(t)dt[/math]

 

[Steven G]

Again, you are finding the differential of both sides. The notation for derivative, in this case, is \(\displaystyle \dfrac{d}{dt}\), the the notation for differential is d

 

[Shiloh]

I think we should point out that, although it look like a fraction, \(\displaystyle \frac{dx}{dx}\) is NOT defined as a fraction but as a limit of fractions. It happens that it can be treated like a fraction so to formalize that by introducing the notions of "differentials", dx, purely symbolic, and dy defined by dy= f'(x)dx. With that notation we can write f'(x) as the fraction dy/dx.