Question

Given x=e^t, y=sint, find the value of d^(2)y/dx^(2) at t=0

Answer 1

I'm just not familiar with what \[\frac{ d ^{2}y }{ dx ^{2} }\]. is that just second derivative???

Answer 2

yes, you have to express t in terms of x in order to be able to have \(y\) given as a function of \(x\).

Answer 3

\(t = \ln(x)\). replace in the expression of \(y\) and start computing..

Answer 4

ok. so i got Sin(lnx). Now, do I put zero in for t.?

Answer 5

i mean x?

Answer 6

no, now you must compute the second derivative. when you're done, make the replacement. (\(t = \ln(x)\) means that if \(t=0\) then \(x=1\))

Answer 7

So do I derive Sin(lnx)/e^t ?

Answer 8

\(y=\sin (t) = \sin (\ln x)\). You derive \(f(x)=\sin(\ln(x))\) with respect to \(x\).

Answer 9

f'(x)= Cos(lnx)/x......

Answer 10

for checking: the first derivative is equal to \(\frac{\cos(\ln(x))}{x}\).

Answer 11

sorry friend, we have formula something like