91影视

Use the definition of the derivative to find f' for each function f.

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

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.

$f\left(x\right)=\frac{\left(3x+1\right){\left(x^4-3\right)}^4}{{\left(x+5\right)}^{-2}{\left(1+x^2\right)}^5}$

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

$f\left(x\right)={\tan }^{-1}\left(\ln x\right)$

If$y=3x^{2}t-t^k$, where x and k are constant, find$\frac{dy}{dt}$

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

$f\left(x\right)=x^2\ln \left(\ln x\right)$

Fill in the blank:$(f+g)\text{'}\left(x\right)=\_\_\_\_\_\_\_\_\_\_.$

Use the differentiation rules developed in this section to find

the derivatives of the functions

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

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.

$f\left(x\right)=\sin 鈦�x,c=\frac{蟺}{2}$

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.

$f\left(x\right)={\left(5x^4-3x^2\right)}^7\left(2x^3+1\right)$

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

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