Question

find the derivative of f(x)=cosπx^2

Answer 1

\[f(x)=\cos(\pi)x^2 or f(x)=\cos(\pi x^2) or f(x)=(\cos(\pi x))^2\]
which is it?

Answer 2

the second one I think because the book doesn't have any parenthesis at all

Answer 3

\[f(x)=\cos(\pi x^2) => f'(x)=(\pi x^2)'[(\cos')(\pi x^2)]=\pi (x^2)'[(\cos')(\pi x^2)]\]

Answer 4

\[f'(x)=\pi (2x)(-\sin(\pi x^2))\]

Answer 5

\[f'(x)=-2\pi x \sin(\pi x^2)\]

Answer 6

what rule did you use?

Answer 7

chain rule
do you not see i took the derivative of the inside and multiplied by derivative of outside?

Answer 8

\[f(x)=h(g(x))=\cos(\pi x^2) => h(x)= \cos(x) , g(x)=\pi x^2\]
\[f'(x)=g'(x)h'(g(x))=2\pi x(-\sin(g(x)))=2\pi x(-\sin(\pi x^2))=-2 \pi x \sin(\pi x^2)\]