Question

If f(x,t)=xt, and x=sin t , find df/dx and df/dt.

Answer 1

since x= sin t
can you express, f(x,t) in terms of t only ?

Answer 2

I don't think that I can here because f is a function of x and t, so they depend on each other?

Answer 3

f(t) = t sin t
now just diff. this w.r.t t to get df/dt

Answer 4

Okay, this one does make sense to me, I get sin(t)+t*cos(t)

Answer 5

correct
similarly ,can u find f only in terms of x ?

Answer 6

t=arcsin(x)? So f(x)=x*arcsin(x)

Answer 7

correct, just diff. this using product rule

Answer 8

Okay, so I cannot just say df/dt=x by differentiating the function f? Using x*arcsin(x), I get df/dt=x/sqrt(1-x^2)+arcsin(x)

Answer 9

no, you can't say that, if you sat that, you are treating "x" as constant
which is not true sin f is the function of both x and t
and your df/dt is also correct :)

Answer 10

Okay, good to know. Thank you! :)

Answer 11

welcome ^_^