Question

finding a multistep derivative

Answer 1

the question is to find (f o g)' at the given x
\[f(u)=\cot \frac{ \pi u }{ 10 },u=g(x)=\pi x, x=\frac{ 1 }{ 4 }\]

Answer 2

what I want to know is pi a constant? so would it be zero?

Answer 3

I substituted in g(x) to get \[\cot \frac{ \pi^2 x}{ 10 }\]

Answer 4

and the derivative I got from that was just \[\sec^2\frac{ 1 }{ 10 }\]

Answer 5

which I am not confident is right

Answer 6

pi is a number, its just a number that cannot be accurately expressed and is consigned to a greek letter instead.

Answer 7

what about the rest of my work?

Answer 8

(fog) = f(g)

f(g) derives to f'(g) * g'

Answer 9

im not too clear on what f and g are ...

Answer 10

f is the cot function g is the pix function

Answer 11

cot(g) derives to -csc^2 (g) * g'

right?

Answer 12

is g = pi(x)/10 ??

Answer 13

you have a "u" in there thats kinda confusing me as far as reading it goes

Answer 14

so just make the u an x instead the book I think just did that for the problem

Answer 15

so \[f(x)=\cot \frac{ \pi x }{ 10 }\]\[g(x)=\pi x\]

Answer 16

lets say ..
\[f(g)=cot(kg)~:~\text{for some constant k.}\]
\[[f(g)]'=-csc(kg)~cot(kg)~kg'\]
since g = pi x
g' = pi
\[[f(g)]'=-csc(kg)~cot(kg)~k(pi)\]

Answer 17

in this case, k = pi/10, its just that k was easer to type lol

Answer 18

I'm still not understanding what you did

Answer 19

@agent0smith