Question

Derivative of 3+xsin(pi(x))

Answer 1

product rule, then chain-rule it

Answer 2

you need the product rule
if y = uv then y' = u'v +uv'

Answer 3

I got y′ = (x pi'(x)cos(pi(x)+ sin(pi(x)) but I am not sure if I did it right.

Answer 4

hmmm derivative of x is 1

Answer 5

other than that, looks ok

Answer 6

wait so what should I change? should I make x=1 instead?

Answer 7

(x pi'(x)cos(pi(x)+ sin(pi(x))
^
that x

Answer 8

I was wondering about that lone x

Answer 9

\(\bf y=3+xsin(\pi x) \quad y'=[1\cdot sin(\pi x)] +[x\cdot cos(\pi x)\cdot \pi]\)