(adsbygoogle = window.adsbygoogle || []).push({}); 1.I'm having trouble using the definition of derivative on algebraic functions involving trig functions. Here's the problem:

I need to find the first and second derivative of f(x) = [tex]x^{2}sin(x) + 2xsin(x)[/tex]

2.I know how to use the definition of derivative, [tex]\stackrel{lim}{h->0}\frac{f(x+h) - f(x)}{h}[/tex], but I was never good at using it when trig functions were involved. I'm guessing the angle addition formula will be involved: sin(x+h) = sin(x)cos(h) + cos(x)sin(h) .

I also know that, if I can manage to get it in this form, [tex]\stackrel{lim}{h->0}\frac{cos(h) - 1}{h} = 0[/tex]

3. I'm stuck at this point:

[tex]\stackrel{lim}{h->0}\frac{(x^2 + hx + h^2)(sin(x)cos(h) + cos(x)sin(h)) - x^2sin(x)}{h}[/tex]

Any help would greatly be appreciated!

EDIT: I should also add that we haven't covered u-substition yet; we have to do this the long way without any shortcuts.

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# Homework Help: Using definition of derivative w/ trig

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