Section 2.3 Homework

 

1.  Differentiate the function.

$f\left(x\right)=2^{80}$

$f‘\left(x\right) = \_\_\_$

 

2. Differentiate the function.

$f\left(x\right) = 5.1x + 2.3$

$f‘\left(x\right) =$

 

3.  Differentiate the function.

$$\begin{gathered} g\left(x\right)=\frac{3}{8}{x}^2–2x+15 \\ g‘\left(x\right) = \end{gathered}$$

 

4.  Differentiate the function.

$$\begin{gathered} g\left(x\right) = x^2(1–7x) \\ g‘\left(x\right) = \_\_\_\_\_\_ \end{gathered}$$

 

 

5.  Differentiate the function.

$F\left(r\right)=\frac{7}{r^3}$

 

6.Differentiate the function.

$R\left(a\right) = {(2a+1)}^2$

$R‘\left(a\right) =$

 

7.   Differentiate the function. 

$$\begin{gathered} y=\frac{6x^2+8x+6}{\sqrt{x}} \\ y‘= \end{gathered}$$

 

 

8.  Differentiate.

$F\left(y\right)=(\frac{1}{y^2}–\frac{3}{y^4})(y+7y^3)$

 

 

9.  Differentiate.

$$\begin{gathered} g\left(x\right)=\frac{9+4x}{1–6x} \\ g‘\left(x\right) = \end{gathered}$$

 

 

10.   Differentiate.

$y=\frac{\sqrt{x}}{6+x}$

$y‘=$

 

11.   Differentiate.

$f\left(t\right) = \frac{\sqrt[3]{t}}{t–3}$

$f‘\left(t\right) =$

 

 

12.  Find an equation of the tangent line to the curve at the given point.

$y=\frac{4x}{x+1}, (3,3)$

y=

 

 

13. Find an equation of the tangent line to the curve at the given point.

$y=3x^3–x^2+5, (2,25)$

y=

 

14.   Find equations of the tangent line and normal line to the curve at the given point.

 

 

15.  Find the first and second derivatives of the function.

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

 

16.    The equation of motion of a particle is 

$s=t^3–12t,$

  where s is in meters and t is in seconds. (Assume t ≥ 0.)

(a) Find the velocity and acceleration as functions of t.

(b) Find the acceleration after 9 s.

(c) Find the acceleration when the velocity is 0.

 

 

17   Find the points on the curve 

$y=2x^3+3x^2–12x+8$

   where the tangent line is horizontal.

 

18.  Find equations of the tangent lines to the curve

$y=\frac{x–1}{x+1}$

that are parallel to the line  x − 2y = 2.

 

19  Find an equation of the normal line to the curve 

$y=\sqrt{x}$

  that is parallel to the line 4x + y = 1.