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.

$f\left(x\right)={\left(5{\left(3x^4-1\right)}^3+3x-1\right)}^{100}$

Fill in the blank:

If $3v^2+xv-1=0$,find$\frac{dx}{dv}.$

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

$f\left(x\right)=\frac{\sqrt{e^x}}{\ln \sqrt{x}}$

Fill in the blank:

$\frac{d}{dx}\left(cos{h}^{-1}x\right)=\_\_\_\_\_\_\_\_\_\_\_.$

Use the differentiation rules developed in this section to find

the derivatives of the functions

$5x^3-2x^2+7$

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.

$f\left(x\right)=x+x^3,c=1$

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

$f\left(x\right)=3{\left({\sin }^{-1}x\right)}^2$

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.

$f\left(x\right)={\left(1-4x\right)}^2{(3x^2+1)}^9$

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.

$f\left(x\right)=\sec 鈦�x,x=0$