1. Calculate f'(x)

$\displaystyle f(x)=tg x \cdot e^{3x}$
$\displaystyle f'(x)=(tg x \cdot e^{3x})'=...$

What rule I can use to solve this? I need examples like this tasks or something

2. Are t and g considered constant?

3. It's tg(x)

4. Is that the tangent function, then?

5. Originally Posted by Ackbeet
Is that the tangent function, then?
Yes.

6. Ah. Standard notation is

$\displaystyle (\tan(x)e^{3x})'.$

What rule do you think would be appropriate here?

7. Yes, mr. Ackbeet it is tan(x)....

Appalling the chain rule...

$\displaystyle f'(x)=(tag x \cdot e^{3x})'= (tan(x))'e^{3x}+tan(x)(e^{3x})'$...

Could you proceed from here...?

8. Well, technically, it's the product rule. But yes, that is the rule to use here. I was hoping Lil would see that on her own.

9. Originally Posted by Ackbeet
Well, technically, it's the product rule. But yes, that is the rule to use here. I was hoping Lil would see that on her own.
ok, it's like $\displaystyle (u\cdot v)'=u'v+uv'$

10. Right.

11. It's correct:
$\displaystyle (tan(x))'=\frac{1}{cos^2x}$
$\displaystyle (e^{3x})'=e^{3x}*3$

12. Correct. So you get what?

13. $\displaystyle =\frac{1}{cos^2x}\cdot e^{3x}+tgx\cdot e^{3x}\cdot 3$

What do next I don't know?

14. How about factoring out the $\displaystyle e^{3x}?$

15. Originally Posted by Ackbeet
How about factoring out the $\displaystyle e^{3x}?$
$\displaystyle 3e^{3x}$?
How first e^{3x} I don't know

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