Question

derivative of 4cos[5pi(x)]
sorry for my terrible syntax..

Answer 1

\[-4\sin(5\pi x)\times 5\pi=-20\pi\sin(5\pi x)\]

Answer 2

but how i got lost in my u-sub

Answer 3

you integrating or differentiating?

Answer 4

diff right? then by the chain rule
\[\frac{d}{dx}[cos(ax)]=-\sin(ax)\times a=-a\sin(ax)\]

Answer 5

oh okay..
wolframalpha was confusing me
thank you

Answer 6

you can write \(u=5\pi x, u'=5\pi\) if you like but it is a waste of time, you should do it in your head
derivative of the outside function evaluated at the inside function time the derivative of the inside function

Answer 7

okay thanks

Answer 8

yw