Question

Find the derivative:

4sec^2 (3pit-3)

do I use product rule or chain rule?

Answer 1

\[4\sec ^{2} (3\pi t - 3)\]

Answer 2

chain rule ?

Answer 3

Mhm! Chain rule indeed.
Outer-most function is the square.

Answer 4

\[\Large\rm \color{royalblue}{4\frac{d}{dt}\sec^2(3\pi t-3)}=4\cdot2\sec(3\pi t-3)\color{royalblue}{\frac{d}{dt}\sec(3\pi t-3)}\]

Answer 5

ok..that looks good...hmm

Answer 6

but i need to take the derv of the inside (3pit -3)

Answer 7

so its 3pi

Answer 8

That's off of the very last chain, you need to do this chain first.\[\large\rm =4\cdot2\sec(3\pi t-3)\color{royalblue}{\frac{d}{dt}\sec(3\pi t-3)}\]\[\large\rm =4\cdot2\sec(3\pi t-3)\color{orangered}{\sec(3\pi t-3)\tan(3\pi t-3)}\color{royalblue}{\frac{d}{dt}(3\pi t-3)}\]But yes, you're correct, you'll get an extra 3pi from applying chain rule a second time.

Answer 9

final answer : \[24 \pi \sec ^{2}(3\pi t-3)\tan(3\pi t-3)\]

Answer 10

@zepdrix

Answer 11

mm yah looks good! c: