91Ó°ÊÓ

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:

Calculate if f(x)=g(x)h(x) then find f'(0)

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 the function

$f\left(x\right)=\sqrt{\tan h^3\left(x^5\right)}$

Fill in the blank:

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

Find the derivatives of the functions:$f\left(x\right)=e^{3\ln x}$

Sketch a graph of the associated slope function ffor each functionf in Exercises 25–30.

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

$f\left(x\right)=\sin \left(\cos \right(sec\left(x\right)\left)\right).$

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.

$f\left(x\right)=\frac{1}{\sqrt{x^2+1}}$

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:

f(x)=g(x)(h(x)+j(x)) find f'(2)

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.

25.$f\left(x\right)=\frac{1}{x},x=-1$