91Ó°ÊÓ

In Problems 21-28, find the indicated derivative. $$ \frac{d}{d t}\left(\frac{(3 t-2)^{3}}{t+5}\right) $$

$$ \text { In Problems } 1-44, \text { find } D_{x} y \text { using the rules of this section. } $$ $$ y=(2 x+1)^{2} $$

Find \(D_{x} y\). $$ y=\sin ^{-1}\left(2 x^{2}\right) $$

Find \(D_{x} y\). $$ y=\arccos \left(e^{x}\right) $$

In Problems 21-28, find the indicated derivative. $$ \frac{d}{d \theta}\left(\sin ^{3} \theta\right) $$

In Problems 23-28, an object is moving along a horizontal coordinate line according to the formula \(s=f(t)\), where \(s\), the directed distance from the origin, is in feet and \(t\) is in seconds. In each case, answer the following questions (see Examples 2 and 3). (a) What are \(v(t)\) and \(a(t)\), the velocity and acceleration, at time \(t\) ? (b) When is the object moving to the right? (c) When is it moving to the left? (d) When is its acceleration negative? (e) Draw a schematic diagram that shows the motion of the object. $$ s=2 t^{3}-6 t+5 $$

$$ \text { In Problems } 1-44, \text { find } D_{x} y \text { using the rules of this section. } $$ $$ y=(-3 x+2)^{2} $$

Find all points on the graph of \(y=\tan ^{2} x\) where the tangent line is horizontal.

Find the indicated derivative. \(f^{\prime}\left(\frac{\pi}{4}\right)\) if \(f(x)=\ln (\cos x)\)

In Problems 23-28, an object is moving along a horizontal coordinate line according to the formula \(s=f(t)\), where \(s\), the directed distance from the origin, is in feet and \(t\) is in seconds. In each case, answer the following questions (see Examples 2 and 3). (a) What are \(v(t)\) and \(a(t)\), the velocity and acceleration, at time \(t\) ? (b) When is the object moving to the right? (c) When is it moving to the left? (d) When is its acceleration negative? (e) Draw a schematic diagram that shows the motion of the object. $$ s=t^{2}+\frac{16}{t}, t>0 $$