Example of Chain Rule 3 - Trig Functions

Calculus: Find the derivative of the following trig functions: (a) f(x) = sin^4(x) + cos(4x), (b) f(x) = sec(x^2 + x + 1), and (c) f(x) = sin(cos(x)).

[MathDoctorBob]

@husamaldean Definitely. Check the Linear Algebra playlist. There are also vectors in the Multivariable Calculus playlist. Which class is math 125? Every college has its own numbering. - Bob

[MathDoctorBob]

Fourth part of a five part series. See Part 1 of the Calculus playlist.

[MathDoctorBob]

I figured as much. What was the second function?

For 5^sec(x), we use the identity 5 equals e^ln(5) and the chain rule applies to e^(ln(5) sec(x)).

That gives ln(5)sec(x)tan(x) 5^(ln(5)sec(x)) = ln(5)sec(x)tan(x) 5^sec(x).

[MathDoctorBob]

:) You're welcome! Definitely let me know how things go.

[MathDoctorBob]

This is notation for (cos(x))^5, so inside = cos(x), outside = u^5. Then apply chain rule.

[MathDoctorBob]

@husamaldean I have about 40 linear algebra videos. Check the website on my channel page; the lists will be easier to search. If you can't find something, I'm happy to add to the playlist. - Bob

[fanmaxis]

Dr. Bob, can you explain how you differentiate the functions 5^sex(x) and ? Thank you.

[Julisauruss]

Can you view 3t^3sec(3t) as (3t^3sec(3t))^1 and just do the derivative of everything in it equation once and multiply it by the original equation?

[imann]

Dude your ripped haha, thank you for explaining this.

[MathDoctorBob]

As a youngster, max at 610, worked with 400 for reps. But hey, you don't even see my legs in these.

[MathDoctorBob]

Chain rule here won't make life easier. (y^1)' = 1(y^0)y' = y', so you are just taking the derivative of the inside.