# Quiz Chapter 02.01: Primer on Differential Calculus

 MULTIPLE CHOICE TEST BACKGROUND DIFFERENTIATION

1. The definition of the first derivative of a function $f \left( x \right)$ is

2. Given $y=5e^{3x}+\sin{\left( x \right)}$, then $dy/dx$ is

3. Given $y=\sin{\left( 2x \right)}$, then $dy/dx$ at $x=3$ most nearly is

4. Given $y=x^{3}\ln{\left( x \right)}$, then $dy/dx$ is

5. The velocity of a body as a function of time is given as $v \left( t \right) = 5e^{-2t} + 4$, where $t$ is in seconds, $v$ is in $m/s$. The acceleration at $t=0.6$ in $m/s^{2}$ is

6. If $x^{2} + 2xy = y^{2}$, then $dy/dx$ is