Question

Find dy/dx at the given point.

Answer 1

\[\cos^2(9y)=x+y\]
at points
\[(\frac{ 2-\pi }{ 4 }) (\frac{ \pi }{ 4 })\]

Answer 2

\[-2\cos(9y)\times \sin(9y)\times 9y'=1+y'\]

Answer 3

you applied the chain rule to cos?

Answer 4

i guess it is better to write
\[-18\cos(9y)\sin(9y)y'=1+y'\] yes it is the chain rule repeatedly

Answer 5

derivative of something squared is two times something
derivative of cosine is - sine
derivative of \(9y\) is \(9y'\) as you are considering \(y\) as a function of \(x\) i.e. \(y=y(x)\)

Answer 6

so now i factor out my y' from the left hand side?

Answer 7

\[y'=\frac{ 1+y' }{ -18\cos(9y)\sin(9y) }\]

Answer 8

confused because if i take my y' and move it to the left hand side, im left with zero which doesnt make sense.

Answer 9

:(