Question

Goodness, what about this one
f(x)=cos(arcsin(9x))

Answer 1

arcsin(9x) is easy, but i'm not sure what to do with the cos out front

Answer 2

you mean write it as a function of \(x\) with no trig?

Answer 3

Yeah, find the derivative

Answer 4

start with
\[\cos(\arcsin(9x))=\frac{1}{\sqrt{1+81x^2}}\] and take the derivative of that

Answer 5

Ummmm, \[\frac{ 1 }{ \sqrt{162x} }\]?

Answer 6

or do i use the quotient rule?

Answer 7

\[\Large\rm \arcsin(9x)=\theta\qquad\to\qquad \sin \theta=9x\]

Answer 8

Pythagorean Theorem to find this missing side.