if u=tan-1(y/x),x=e^t-e^-t and y=e^t+e^-t then find du/dt
You asked:
Given the following equations: \[\begin{aligned}u &= \tan\left( -1 \right) \cdot \frac{y}{x}\\ x &= {e}^{t} - {e}^{-t}\\ y &= {e}^{t} + {e}^{-t}\end{aligned}\] Evaluate \(\frac{d}{dt}\left[u\left( t \right)\right]\).
MathBot Answer:
\[\frac{d}{d t} u{\left(t \right)} = \frac{d}{d t} u{\left(t \right)}\]