This is the problem I have f(x)= x^3 ( sec(x) )

And this is what I think the answer is. Is it correct? If so could I possibly just distribute the sec(x) through (sec(x) tan(x) )? Thanks ahead of time.
f'(x)= 6x^2 (sec(x)) (sec(x) tan(x))

2. Originally Posted by CalcNewb
This is the problem I have f(x)= x^3 ( sec(x) )

And this is what I think the answer is. Is it correct? If so could I possibly just distribute the sec(x) through (sec(x) tan(x) )? Thanks ahead of time.
f'(x)= 6x^2 (sec(x)) (sec(x) tan(x))
You need to apply product rule here.

You should end up with $\displaystyle f'(x)=3x^2\sec(x)+x^3\sec(x)\cdot\sec(x)\tan(x)=3x ^2\sec(x)+x^3\sec^2(x)\tan(x)$

Does this make sense?

--Chris

3. Originally Posted by Chris L T521
You need to apply product rule here.

You should end up with $\displaystyle f'(x)=3x^2\sec(x)+x^3\sec(x)\cdot\sec(x)\tan(x)=3x ^2\sec(x)+x^3\sec^2(x)\tan(x)$

Does this make sense?

--Chris
ok yes I do understand how to use the product rule. I used the product rule but got something totally different. Let me try to show you my steps.

"first times derivative of second + second times derivative of the first" this is what our calc teacher told us to remember for product rule. so here it goes
D=derivative

x^3 D(sec(x)) + sec(x) D(x^3)
so I get

X^3 (sec(x) tan(x)) + sec(x) (3x^2)

this is almost what you have I just dont see how you got the other sec^2(x)

4. Originally Posted by CalcNewb
ok yes I do understand how to use the product rule. I used the product rule but got something totally different. Let me try to show you my steps.

"first times derivative of second + second times derivative of the first" this is what our calc teacher told us to remember for product rule. so here it goes
D=derivative

x^3 D(sec(x)) + sec(x) D(x^3)
so I get

X^3 (sec(x) tan(x)) + sec(x) (3x^2)

this is almost what you have I just dont see how you got the other sec^2(x)
Oh...woops!

You're right...it should just be $\displaystyle x^3\sec(x)\tan(x)+3x^2\sec(x)$

I was probably in a hurry and as a result, made a tiny mistake there.

--Chris

5. Originally Posted by Chris L T521
Oh...woops!

You're right...it should just be $\displaystyle x^3\sec(x)\tan(x)+3x^2\sec(x)$

I was probably in a hurry and as a result, made a tiny mistake there.