Question

Find the differential dy for y =cos(pix) and evaluate it x=1/3 and dx=-.02 and round your results to 3 decimal places.

Answer 1

\[\frac{dy}{dx} = y'(x) \rightarrow dy=y'(x)dx\]

Answer 2

\[
y = \cos(\pi x) \rightarrow y'(x) = \pi\cos(\pi x)
\]

Answer 3

\[
\rightarrow dy = \pi \cos(\pi x)dx
\]

Answer 4

-pi sin(pi*x)

Answer 5

oops, yeah..

Answer 6

\[y = \cos(\pi x) \rightarrow y'(x) = -\pi\sin(\pi x)\]
\[\rightarrow dy = -\pi \sin(\pi x)dx\]

Answer 7

then plug in the x and dx correct?

Answer 8

yeah

Answer 9

i get dy to be .054 is there anyway to check if its correct