- #1

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## Homework Statement

Use the approximate relationship to prove:

Δf~[itex]\frac{df}{dx}[/itex]Δx

a) [itex]\frac{dx^{n}}{dx}[/itex]= nx

^{n-1}

b)[itex]\frac{dcos(θ)}{dθ}[/itex]=-sin(θ)

## Homework Equations

a)N/a?? I'm not sure if I need any other equations than the one given.

b) sin(ε)~ε and cos(ε)~1 when ε<<1.

## The Attempt at a Solution

a) So I'm honestly quite lost and know that my attempt is going to be far off.

I thought maybe I could sub in the values into the given equation:

f2-f1~df/dx (x2-x1) (because they are deltas)

x

^{n}-x~[itex]\frac{dx^{n}}{dx}[/itex](Δn)

x

^{n-1}~[itex]\frac{dx^{n}}{dx}[/itex](Δn)

But now I have no clue what I'm doing again and I know what I'm doing doesn't make much sense. I honestly haven't even attempted part (b) because I don't understand what to do with part (a). Just to be clear I'm not looking for help on part (b) yet until I try to attempt the problem. I'm just looking for help with part (a) so that I can try to do part (b) afterwards. Can someone help explain to me how I am suppose to use that formula?