Section 2.5 Homework

1.  Find the derivative of the function.

$$\begin{gathered} F\left(x\right)={(5x^6+8x^3)}^4 \\ F‘\left(x\right) = \end{gathered}$$

2. Find the derivative of the function.

$f\left(x\right) = \sqrt{5x+4}$

f'(x) =

3. Find the derivative of the function.

$f\left(\theta \right) = \cos \left({\theta }^2\right)$

$f‘\left(\theta \right)=$

4.  Find the derivative of the function.

$f\left(t\right)=t \sin \left(\mathrm{\pi t}\right)$

f'(t) =

5. Find the derivative of the function.

$h\left(t\right)={(t+5)}^{2/3}{(2t^2–1)}^3$

h'(t)=

6. Find the derivative of the function.

$y=\sqrt{\frac{x}{x+5}}$

y’=

7. Find the derivative of the function.

$f\left(t\right)=\sqrt{\frac{t}{t^2+3}}$

f'(t) =

8. Find the derivative of the function.

$y=x \sin \frac{8}{x}$

y'(x) =

9.  Find all points on the graph of the function 

  at which the tangent line is horizontal. (Use n as your arbitrary integer.)

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

$y=\sin \left(\sin \right(x\left)\right), (3\mathrm{\pi },0)$