#can someone explain these questions about cvain rule
iron meteor
slim martenBOT
gentle pier
so chain rule is, derivative of inner function * derivative of outer function
gentle pier
ahh you got the first part nice
iron meteor
The second derivative is fucking me
gentle pier
yeah that looks ridiculous
hmm okay
okay so algebraically, F'(x) = 2xf(x)+x^2f'(x)
so F'(1) = 2(1)f(1) +1f'(1)
=2*2+5?
iron meteor
Wait my second derivative is right
gentle pier
so 9 i think
knotty arrow
part (b), first derivative missing something. Once you have that, try the 2nd derivative again. (2 x) (2 x) by itself just doesn't work in this problem. The other piece, while having pieces in the right place, has another issue.
part c answer is not 9.
Try working out derivative with f(x). Once you have it written out, then plug in the known values provided.
ronush's work is basically part of F '(x). It's missing a major piece.
F(x) = f (x^2 * f(x) )
ronush work handles d/dx (x^2 * f(x) ).
What about the rest of the chain rule ?
gentle pier
ohhhhhh,
||all of that * f'(x^2(f)x)||
knotty arrow
g is an unknown function. we don't have info on it.
The chain rule:
h(x) = f ( g(x) )
h ' (x) = g ' (x) f ' ( g(x) )
iron meteor
Wait im finding g? I thought i was just deriving f(x)
X squared is f(x)?
So then that derivative is 2x
knotty arrow
Let me see if I can break it down with a picture...
we definitely want f '(x). The chain rule makes us break this up into pieces. Takes a while to feel automatic with the chain rule.
To make g(x^2), we would take g(x) (whatever it is) and replace every x with x^2.
The chain rule gives us a way to get the derivative when we take one function and put it inside of another one. In this case, x^2 is put into g(x).
iron meteor
.solved