91影视

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.

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

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.

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

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.

$f\left(x\right)=\cos 鈦�x,x=0$

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

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

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

Fill in the blank:

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

Use the differentiation rules developed in this section to find

the derivatives of the functions

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

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.

$f\left(x\right)=\tan 鈦�x,x=0$

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.

$f\left(x\right)=x+x^3,c=0$

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

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