Trigonometric Identity Question (I am gonna use this many times)

[cinder pewter]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations

[humble yacht]

That's correct. Though, probably easier to leave it factored like this:
f'(x) = 2((x + 1)cos(x) - (x - 1)sin(x))

[graceful inlet]

How do I solve part b? The f'(3)

[humble yacht]

Substitute x = 3 into the expression for f'(x).

[graceful inlet]

I know that much, but how do I solve it. Like go from there. The answer is gonna be a decimal but I have no idea what to do

[humble yacht]

No need to do anything.
f'(3) = 2(4cos(3) - 2sin(3)) = 8cos(3) - 4sin(3)

That's it.

[graceful inlet]

How did you do that? That was indeed the answer...

I feel dumb

[humble yacht]

I just substituted x = 3.

[graceful inlet]

Oh my god now I see it 💀

That was so much easier than I saw it as

[humble yacht]

The equation of the tangent to f(x) at x = a is:
y = f'(a)(x - a) + f(a)
So, m = f'(a), b = f(a) - af'(a).

[cursive briar]

Note that the derivative of sin is cos

[graceful inlet]

I am just going to work on my english stuff and go to the math center and my college tomorrow. Though I will prolly get some help with my other assignment before that

[cursive briar]

Generally, to say it in words instead of equations, for the tangent line of a curve f at a given point Q(w|z), youll:

1. find f(w)=z, such that you now know the point at which the tangent intersects with the curve f: Q(w|z),
2. calculated the derivative f’ of the curve and calculate m=f’(w), such that you now know the slope of the tangent at the given point.
3. Now you can solve for b, where the tangent is y=mx+b since you already know m and you know a point on the tangent Q(w|z) by plugging in w and z:
   z=mw+b
   b=z-mw=f(w)-wf’(w)

@graceful inlet

[graceful inlet]

You just made it worse 😭

I barely understand anything and now it got more confusing