How to derive higher order derivatives

[fossil condor]

I'm confused with deriving thisss

[lusty pelican]

second derivative means the derivative of the derivative

third derivative means the derivative of the derivative of the derivative

so on

[fossil condor]

kinda familiar to it, the problem is... I'm confused with the given problem

[lusty pelican]

have you learned about the chain rule yet

[fossil condor]

well yeah

[lusty pelican]

it’s just that

except it’s combined with the product and quotient rules

am lazy to solve sry

[fossil condor]

it's alright, I'm just trying to learn it

[plain vapor]

Try the leibnitz Theorem

[wide hemlock]

🤢🤢🤢🤢

[plain vapor]

I know it looks horrendous

[wide hemlock]

I mean it’s pretty tame and satisfying that it’s a binomial expansion but in practice it’s just annoying.

[fossil condor]

that looks like hell

[wide hemlock]

Like Fa Di Bruno is WAY WAY worse……..

[plain vapor]

HELL NAW

[lethal briar]

you just need to know

• product rule
• derivatives of e^f(x)
• derivatives of cos(f(x))
• power rule
• derivatives of ln[f(x)]
• (not entirely necessary, but could be used: quotient rule)

if you know all 5 you should solve this problem easily