Question

Derivative of the sine and cosine functions. First Derivative. How can I simplify this expression ?

Answer 1

Answer:

The first derivative equals

sin2x .

Explanation:

This is equivalent to saying

y=(sin(π−x))(sin(π−x))

We can expand

sin(π−x) using sin(A−B)=sinAcosB−sinBcosA

y=(sinπcosx−sinxcosπ)(sinπcosx−sinxcosπ)

y=(0(cosx)−sinx(1))((0)cosx−(−1)sinx)

y=(sinx)(sinx)

y=(sinx)2

Now use the chain rule to differentiate. We let y=u2 and u=sinx

. Then dy

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Hopefully this helps!