91影视

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

$f\left(x\right)=\sqrt{3x-4{(2x+1)}^6}$

Use (a) the h鈫�0 definition of the derivative and then (b) the z鈫抍 definition of the derivative to find f'(c) for each function f and value x = c.

$f\left(x\right)=\sin 鈦�x,x=0$

For each function f and value $x=c$in Exercises 35鈥�44, use a sequence of approximations to estimate $f\text{'}\left(c\right)$. Illustrate your work with an appropriate sequence of graphs of secant lines.

$f\left(x\right)=4-x^2,c=1$

Fill in the blanks to differentiate each of the given basic functions. You may assume that k, m, and b are appropriate constants:

$\frac{d}{dx}\left(\cos hx\right)$

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

$f\left(x\right)=\sin \left(\ln x\right).$

Find a function $f$that has the given derivative $f\text{'}$ and value f(c).

$f\text{'}\left(x\right)=\frac{1}{1-4x^2},f\left(0\right)=0$

Find the derivatives of each of functions in Exercises 17鈥�44. In some cases it may be convenient to do some preliminary algebra.

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

Fill in the blank:

$\frac{d}{dx}\left(\tan hx\right)=\_\_\_\_\_\_\_\_.$

Use the differentiation rules developed in this section to find

the derivatives of the functions

$f\left(x\right)=2x-3+4x^2$

For each function f and value $x=c$in Exercises 35鈥�44, use a sequence of approximations to estimate $f\text{'}\left(c\right)$. Illustrate your work with an appropriate sequence of graphs of secant lines.

$f\left(x\right)=4-x^2,c=0$