Find the derivative of the function. \

$$f(x)=\left(9-x^2\right)^{2 / 3}$$

Use the utility to graph the function and its tangent line in the same viewing window.
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$

Find an equation of the tangent line to the graph of the function at the given point
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$

Use a graphing utility to find the derivative of the function at the given point
$s(t)=\dfrac{(4-2 t) \sqrt{1+t}}{3}, \quad\left(0, \dfrac{4}{3}\right)$

Use a computer algebra system to find the second derivative of the function. \

$$f(t)=\dfrac{t}{(1-t)^2}$$

Use the utility to graph the function and its tangent line in the same viewing window. \

$$f(x)=\sqrt{x}(2-x)^2, \quad(4,8)$$

Find an equation of the tangent line to the graph of the function at the given point, \

$$f(x)=\sqrt{x}(2-x)^2, \quad(4,8)$$

Use a graphing utility to find the derivative of the function at the given point \

$$f(x)=\sqrt{x}(2-x)^2, \quad(4,8)$$

Find the second derivative of the function.
$y=\sin ^2 x$

Use the utility to graph the function and its tangent line in the same viewing window. \

$$g(t)=\dfrac{3 t^2}{\sqrt{t^2+2 t-1}}, \quad\left(\dfrac{1}{2}, \dfrac{3}{2}\right)$$

Find an equation of the tangent line to the graph of the function at the given point
$g(t)=\dfrac{3 t^2}{\sqrt{t^2+2 t-1}}, \quad\left(\dfrac{1}{2}, \dfrac{3}{2}\right)$

Use a graphing utility to find the derivative of the function at the given point
$g(t)=\dfrac{3 t^2}{\sqrt{t^2+2 t-1}}, \quad\left(\dfrac{1}{2}, \dfrac{3}{2}\right)$

Find the second derivative of the function. \

$$f(x)=\cot x$$

For $f(x)=\sec ^2 x$ and $g(x)=\tan ^2 x$, show that

$$f^{\prime}(x)=g^{\prime}(x) .$$