91Ó°ÊÓ

Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.

$f\left(x\right)=3secx\tan x.$

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f\left(x\right)=x{(3x^2+1)}^9$

In Exercises 21–24, sketch the graph of a function f that has the listed characteristics.
$$\begin{gathered} f(-1)=2; \\ f\text{'}(-1)=3; \\ f\left(1\right)=-2; \\ f\text{'}\left(1\right)=3 \end{gathered}$$

Suppose g(x), h(x), and j(x) are differentiable functions with the values of the function and its derivative given in the following table:

Find if f(x)= 3j(x)-2h(x) Find f'(3)

: Find the derivatives of the function

$f\left(x\right)=x^x$

Fill in the blank:

$\frac{d}{dx}\left(\ln \left|x\right|\right)=---$

Find the derivatives of the functions:$f\left(x\right)=\frac{e^x\ln x}{x^2−1}$

In Exercises 21–24, sketch the graph of a function f that has the listed characteristics.
$$\begin{gathered} f\text{'}(-2)=2; \\ f\text{'}\left(0\right)=1; \\ f\left(1\right)=-5 \end{gathered}$$

Use (a) the $h→0$definition of the derivative and then

(b) the $z→c$definition of the derivative to find $f\text{'}\left(c\right)$ for each function f and value $x=c$ in Exercises 23–38.

24.$f\left(x\right)=x^3,x=1$

Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.

$f\left(x\right)=3^{x}secx+17.$