differentiation

[austere flame]

can someone help with understand why xln2 = ln2 i thought it was x/2

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[rocky geode]

what is the derivative of x times a constant?

[austere flame]

ln2

[rocky geode]

yeah in this case since the constant is ln2 the derivative of xln2 is ln2

[austere flame]

is that a rule?

like this is it 1/3x+5 because of the linear equation after ln?

[rocky geode]

it just follows the derivative rule that the derivative of a constant times a function is the constant times the derivative

no because that is not a constant

[austere flame]

what if it was ln2x

[rocky geode]

how familiar are you with derivatives?

[austere flame]

would that be 1/2x

[austere flame]

decent

[rocky geode]

yeah that would be 1/2x * 2

[austere flame]

but this one is confusing me

[rocky geode]

so just 1/x

[austere flame]

wait what does a constant mean

[rocky geode]

a constant is anything that is independent of your variable

so if you have a function f(x) and multiply it by like 2 since 2 doesnt have affect x at all

it is a constant

[austere flame]

oh alright ty

[austere flame]

u see if the 2 would change to a y

so it would be xlny

how would u differentiate that by product rule?

[rocky geode]

if you doing the derivative with respect to x it doesnt change

if y is a constant with respect to x

if y is a function of x you would product rule and chain rule

Do you know the product rule?

[austere flame]

yes

this was the question

how would i know if y is a constant or a function

[rocky geode]

if you see a variable = another then it is a not a constant

[austere flame]

oh ok

what about this one

[rocky geode]

What do you think is y a constant or variable with respect to x

[austere flame]

is it a constant

[rocky geode]

No

[austere flame]

oh 😭

[rocky geode]

it you see anything like y = x or somethingy = something x or anything similar

it is not a constant with respect to x

try solving the problem with the chain rule and product rule

[austere flame]

oh ok

oh u cant differentiate ln2

so it would just be ln2

[rocky geode]

can you show me the steps you took?

[austere flame]

when u use product rule for xln2

[rocky geode]

yeah

[austere flame]

i see i get it