Question

Derivative of (3x^2)(secx)

Answer 1

Find the derivative of

y = 3x² · sec x


To differentiate this function, apply the product rule:

y = u · v ⇒ y' = u' · v + u · v'


So, for this one, you have

y' = (3x²)' · sec x + 3x² · (sec x)'

y' = 3 · (x²)' · sec x + 3x² · (sec x)'


The derivative of x² is 2x:

y' = 3 · 2x · sec x + 3x² · (sec x)'

y' = 6x · sec x + 3x² · (sec x)'


The derivative of sec x is sec x · tan x:

y' = 6x · sec x + 3x² · (sec x · tan x)


Take out the common factor 3x · sec x:

y' = (3x · sec x) · 2 + (3x · sec x) · x · tan x

y' = (3x · sec x) · (2 + x · tan x) <——— this is the answer.


I hope this helps. =)

Answer 2

Hope this helps you.