Question

A poiny is moving along the graph of y= 1/(1+x^2) such that dx/dt = 2cm/s (change in x with respect to time). Find dy/dt for x=2 and x=-2

Answer 1

\[\frac{dy}{dt} = \frac{dy}{dx}*\frac{dx}{dt} = 2\frac{dy}{dx}\]

Answer 2

for dy/dx use chain rule
\[f'(u(x)) = u'(x)*f'(u)\]
\[f(u) = \frac{1}{u}\]
\[u(x) = 1+x^{2}\]