Question

How do you differentiate y=cospixsinpix

Answer 1

first reduce the trig. function

Answer 2

Would this use the product rule?

Answer 3

Yes

Answer 4

I'm tempted to use this: \(\sin(2x) = 2\sin(x)\cos(x)\), entirely avoiding the Product Rule for the derivative.

Answer 5

\[y=\frac{2\cos \pi xsin \pi x}{2}\]
\[y=\frac{sin2 \pi x}{2}\]
now apply chain rule

Answer 6

\(\cfrac{d}{dx} (\cos \pi x)(\sin \pi x)\)

Differentiating by using Product rule :
\(\large\cos(\pi x)(\cos \pi x ) \ pi + \sin \pi x (-\ sin \pi x ) \pi\)