(Calc 1) Derivative of Trig function

[wide silo]

So I get very confused with how to take the derivative of a trig function as sometimes (for example) I’d get asked to take the derivative of cos and end up with -sin and cos to the end of it, ik it has to do with the chain rule but sometimes I don’t even with that result and I just would appreciate some clarification as Ik it has to do with what’s in the parentheses and if the trig function is raised to smth

[wide silo]

like ts is killing me

[ornate narwhal]

Think of it as outer and inner functions

The outer function is something to the power 4

Derivative of that is 4 times something to power 3

Now you gotta differentiate the inner function

You’ll get a hang of it once you do a few problems

[wide silo]

so in this case do I consider 4cos as the outer function?

so then -4sin(4-x^3) * (-3x^2)?

[ornate narwhal]

Yes exactly

[wide silo]

ok ok

and for this one i’m kinda confused where I’d put the -1/2

[wide silo]

(what in raising)

[ornate narwhal]

Think of it as cosx to the power of half

Outer function would be something to the half power and inner would be cosx

[wide silo]

bc this is what I got it

i just combined it

so would I just keep the ^-1/2 to the cos?

or both

i’m confuzzed

😓

sorry

[ornate narwhal]

Just that

[ornate narwhal]

It’s correct

[wide silo]

AYYY

i’m getting the hang of this

[ornate narwhal]

Goodjob matey

[wide silo]

u rlly taught me more in like 5 minutes than my teacher did 2 weeks

[ornate narwhal]

Proud of you

[wide silo]

thank u brotato

[ornate narwhal]

Thanks man glad to help 😭😭

[wide silo]

so i always keep what I originally had (like w the cos^-1/2)

[ornate narwhal]

Yes sir

[wide silo]

i don’t distribute it to the chain ruled part

oh ok thank u thank u

[ornate narwhal]

Yes exactly the derivative of the outer function doesn’t affect the inner one