Show each step of your work and fully simplify each expression.
Turn in your answers in class on a physical piece of paper.
Staple multiple sheets together.
Feel free to use Desmos for graphing.
Answer the following:
Differentiate the following:
$f(x) = \sec x$
$f(x) = \cot x$
$f(x) = \dfrac{\sec x}{1 + \tan x}$
$f(t) = e^t\sin t$
$f(x) = (x^4 + 4x^2)e^x$
$y' = \dfrac{e^x}{1 + x}$
$f(t) = \dfrac{t - \sqrt{t}}{t^{1/3}}$
$y = e^{\sqrt{x}}$
$f(x) = (3x - x^3)^23$
$f(x) = \sqrt[3]{1 + \tan x}$
$f(x) = xe^{-2x}$
$f(x) = (3x + 2)^3(4x^2 + 3)^4$
$y = \sqrt{x + \sqrt{ x + \sqrt{x}}}$
$f(x) = 2^{\sin \pi x}$
$f(x) = \sqrt{\dfrac{x}{x^2 + 4}}$
$f(x) = e^{e^x}$
$f(x) = \sin x + \sin^2 x$
Find the equation of the tangent line to the curve at the given point.
$y = (1 + 2x)^{10}, \qquad (0, 1)$
$y = \sin(\sin(x)), \qquad (\pi, 0)$
Recall the BAC example from 3.1. The concentration function is \[C(t) = 0.0225te^{-0.0467t}\] How rapidly is the BAC decreasing a half hour after ingestion?
Find $dy/dx$ with implicit differentiation for the equation \[x^3 + y^3 + x^2 + y = 1\]
Consider the equation $x^{2/3} + y^{2/3} = 4$. Find the equation of the tangent line at the point $(-3\sqrt{3}, 1)$.