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abstrakt!

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## Homework Statement

Find the derivative when [itex]y(x)=\sin x[/itex]

## The Attempt at a Solution

[itex]\frac{dy}{dx} \ = \ limit \ of \ \frac {\Delta y}{\Delta x} \ = \ \lim h \rightarrow 0 \ \frac{\sin(x+h)-\sin x}{h}[/itex]

[itex]\sin(x+h)=\sin x \cos h + \cos x \sin h[/itex]

[itex]\frac{\Delta y}{\Delta x} \ = \ \frac {\sin x \cos h + \cos x \sin h-\sin x}{h} \ = \ \sin x ( \frac{\cos h-1}{h}) + \cos x (\frac{\sin h}{h})[/itex]