Question

1.) Use the product rule to find the derivative of

(−10x⁶−7x⁹)(3e^x+3)

2.) If f(t)=(t²+5t+8)(3t²+2) find f'(t)
   
Find f'(4)

3.) Find the derivative of the function
g(x)=(4x²+x−5)e^x

g'(x)=

4.) If f(x)=(5−x²) / (8+x²) find:

f'(x)=

5.) If f(x)=(6x²+3x+4) / (√x) , .  then:

f'(x) =    

f'(1) =

6.) Find the derivative of the function g(x)=(e^x) / (3+4x)

g'(x)=

7.)

Differentiate: y=(ln(x)) /( x⁶)

(dy) / (dx) =

8.) Given that
f(x)=x⁷h(x)
h(−1)=2
h'(−1)=5

Calculate f'(−1)

9.) The dose-response for a specific drug is f(x)=(100x²) / (x²+0.14) where f(x) is the percent of relief obtained from a dose of x grams of a drug, where 0≤x≤1.5

Find f'(0.7)

f'(0.7) =

and select the appropriate units.

a)Grams per percent relief

b)Percent relief per gram

c)Percent relief

d)Grams

10.)Let f(x)= (x) / (x+6) . Find the values of x where f'(x)=5

Give exact answers (not decimal approximations).


The greater solution is x=   
The lesser solution is x=  

Answer 1