# Math Help - Derivatives of trig functions

1. ## Derivatives of trig functions

So I just typed out 4 of my problems with work and somehow the firefox closed so Im not gonna do that again since it took me forever.... Ill just give original and my answer and see whats wrong.

5. lim x→0 tan(x) / 2x Evaluate the limit.
Did not know how to approach.

Any help on any of these problems is GREATLY appreciated!!!

2. Got #1 So scratch that.

3. got #4 now too....

No 2: $5x(sinx+cosx) = 5xsinx+5xcosx$

use product rule on both 5xsinx and 5xcosx, you get:

$f'(x) = 5sinx+5xcosx+5cosx-5xsinx$

Now do the rest....

No 3: $2xsin(x)cos(x) = x \times 2sinxcosx = x sin(2x)$..

Now use the product rule.. Show your work if you are stuck

5. ok great thanks, solved 2 and 3 now just cant figure out this #5, ive gotten undefined by finding derivative and getting sin(0) on denominator...

6. as x-> 0, the function becomes undeifned...

Used LHopital's Rule.. Take derivatives of numerator and the denominator:

so

$\frac{1}{2} \lim_{x \to 0} \frac{\frac{d (tanx)}{dx}}{\frac{dx}{dx}} = \frac{1}{2} \lim_{x \to 0} \frac{sec^{2}(x)}{1}}$

So,.....