differentiate (tan3x)^3 (2 Viewers)

[kr73114]

^^

 

[blackops23]

3(sec^2 3x)

don't quote me on this

 

[ninetypercent]

use the chain ruleeeeeeeeeee

so dy/dx = dy/du x du/dx

y = u^3
dy/du = 3u^2

u = tan3x
du/dx = 3sec^2(3x)

dy/dx = 3u^2 x 3sec^2(3x)
= 9(tan3x)^2(sec3x)^2

 

[kr73114]

oh yea function of a function rule
wouldnt that be...
3(tan^2 3x)(sec^2 3x)
not sure

 

[kr73114]

use the chain ruleeeeeeeeeee

so dy/dx = dy/du x du/dx

y = u^3
dy/du = 3u^2

u = tan3x
du/dx = 3sec^2(3x)

dy/dx = 3u^2 x 3sec^2(3x)
= 9(tan3x)^2(sec3x)^2

yeh thanks

 

[jamesfirst]

(tan3x)^3

f(x) = tan3x
f ' (x) = 3sec^2 3x

dy/dx = 3 x (3sec^2 3x) x (tan3x)^2
= (9sec^2 3x)(tan3x)^2