91Ó°ÊÓ

Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.

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

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

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

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 in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.

$f\left(x\right)=\frac{1-6x^3}{3}$

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

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

Use the definition of the derivative to find $f\text{'}$for each function $f$in Exercises 34-59

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

A bowling ball dropped from a height of $400$feet will be $s\left(t\right)=400-16t^2$feet from the ground after $t$seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

When the bowling ball is first dropped, with $h=0.5,$$h=0.25,andh=0.1$

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.

$f\left(x\right)={\left(x^4-\sqrt{3-4x}\right)}^8+5x$

Describe the derivatives of each of the piecewise-defined functions in Exercises 45–48.

$f\left(x\right)=\{2^x,\mathrm{if}x≤-2;\frac{1}{x^2},\mathrm{if}x>-2\}$

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

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