Is it always permissible to simplify an expression before taking the derivative of a function...?

Question

or might the first derivative of that function be different? If the answer can be different, please cite an example.

Answer 1

If you can simplify it and make it simpler, then simplify it first.
Example 1,
y = 2sinx cosx
Without simplification:
y' = 2(cosx cosx - sinx sinx) = 2cos(2x)

or
Simplify first,
y = sin(2x)
y' = cos(2x)(2) = 2cos(2x)

Answer 2

the respond is certain, as the two purposes are equivalent. yet in addition, there's an important greater effective piece of tips, which you will use interior the destiny. Say your functionality is f(x) = (x+a million)/(x+a million) of course you could cancel out, so f(x) = a million Taking the spinoff of it somewhat is.... 0 yet you're in certainty lacking some thing. for the unique (uncancelled) functionality, if x=-a million, the functionality would not exist. subsequently in case you cancel, you may desire to undergo in concepts tips like this, and contain it once you graph, or do greater artwork with it (differential equations exceedingly).

Answer 3

Just be sure that when you reduce you do not remove a point of discontinuity, where the derivative would not exist, as in
f(x) = (x^2-4)/(x-2) which simplifies to x+2. Finding f ' (x) if f(x) = x+2 is just 1 - no indication of missing point

Answer 4

When you simplify, you are just rewriting it as something equal.

So yes, you CAN always simplify.

Usually but not always, it is helpful to simplify.

HOWEVER, the domain has to stay the same. So x^2/x = x wherever it is defined, but it is undefined at x=0, while x is defined at x = 0.