Question

Find the equation of the tangent line to the graph of the given fxn at (0,36) on the graph of the fxn.
f(x)=37-sec^3(2x)

Answer 1

Do you know how to find the derivative of f(x)?

Answer 2

That's my problem. I think I'm messing up somewhere there.

Answer 3

\[
f'(x)=-6 \tan (2 x) \sec ^3(2 x)

\]

Answer 4

uhhh

Answer 5

why isn't it tan^3 and where did you get -6?

Answer 6

The way to understand it is to put
\[
u(x)=\sec(2x)\\
f(x)=37 -u(x)^3\\
f'(x) = - 3 u(x)^2 u'(x)
\]
Do you understand the steps above?

Answer 7

now
\[
u'(x) =2\sec(2x) \tan(2 x)
\]
Replace and you are done

Answer 8

not sure where you got u'(x)

Answer 9

What is the derivative of sec(2 x)?

Answer 10

2 cos 2x?

Answer 11

oh sorry. that was sin 2x

Answer 12

No. The derivative of sec is sec tan

Answer 13

ik.

Answer 14

I meant:
f(x)=−3u(x)2u′(x) <----
I thought power rule would just be
f(x)=−3u(x)2

Answer 15

So the derivative of \(\sec(2x)\) is \( 2 \sec(2 x) \tan(2 x)\)

Answer 16

The power rule is 3 u^2 u'

Answer 17

How is that possible?
http://www.mathwords.com/p/p_assets/p97.gif

Answer 18

In summary
\[
u(x)=\sec(2x)\\
f(x)=37 -u(x)^3\\
f'(x) = - 3 u(x)^2 u'(x)\\
u'(x) =2\sec(2x) \tan(2 x)\\
f'(x)=-6 \tan (2 x) \sec ^3(2 x)
\]

Answer 19

I don't understand that, so could you use the chain rule?

Answer 20

Remember that the we have here u(x)^3 and not x^3

Answer 21

Read about the power rule and come back to this problem

Answer 22

The power rule states that if u is a function of x then the derivative of
(\ u^n\) is \( n u^{n-1} u'\)

Answer 23

Okay. I understand how you did it.

Answer 24

But can I use the chain rule?

Answer 25

You are using both the chain rule and the power rule