Calculus 1

Find the derivative of the following function $y = x^{\frac{2}{x}}$

Find the derivative of the following function

$y = \sqrt{(x^2 + 1){(x - 1)}^2}$

Determine $\frac{dy}{dx}$ for the following function

$y = \sqrt{\frac{1}{x (x + 1)}}$

Use logarithmic differentiation to find the first derivative of the function

$y = x^{x + 1}$

Find the derivative of $y = x^{\sin{(x)}}$

Find the derivative of ${(\ln{x})}^{(\ln{(x)})}$

Use logarithmic differentiation to find the derivative of the following function

$y = \frac{(x - 1)(x + 2)(x + 3)(x - 4)}{(x + 5)(x - 3)}$

Find the critical points of the function

$f(x) = \frac{5}{{(x^2 - 4x)}^2}$

For the following function draw a rough sketch of the graph for the 3 cases

$f(x) = \frac{(x - a)}{(x - b)(x - c)}$

Case 1: a < b, c

Case 2: b < a < c

Case 3: b, c < a

Find and classify the critical points of the following function

$f(x) = x^3 - 3x^2 - 9x + 2$

$y = x^{2/3}(2-x)$

Find: A. The critical values of x? B. The x coordinate of the local maximum

Find the critical points of the following function

$f(x) = 6x^5 + 33x^4 - 30x^3 + 100$

Find the critical numbers for the following function

$f(x) = \ln{(x^{2})} + 1.5x$

Find the critical numbers of the function

$f(x) = x^2 - 4x$

Find the critical numbers for the following function $f(x) = x^{\frac{2}{3}}$

Draw a rough graph of the following function using the critical numbers

$f(x) = \frac{2}{3}x^3 + \frac{9}{2}x^2 - 5x - 17$

Find the inflection points for the following function and determine intervals of concave up and concave down on the graph

$f(x) = \ln{(1 - \ln{(x)})}$

Find the inflection points and intervals of concavity for the following function

$y = \frac{x^2 + 1}{x^2}$

Use the 2nd Derivative Test to find the inflection points and intervals of concavity for the following function

$f(x) = x^{3}(x - 4)$

Find all points of inflection and discuss the concavity over different intervals for the following function

$f(x) = x^3 - 6x^2 + 12x$