Difference between revisions of "009A Sample Midterm 3, Problem 5"

Revision as of 16:31, 17 February 2017

Find the derivatives of the following functions. Do not simplify.

a)

f(x)={\frac {(3x-5)(-x^{-2}+4x)}{x^{\frac {4}{5}}}}

b)

g(x)={\sqrt {x}}+{\frac {1}{\sqrt {x}}}+{\sqrt {\pi }}

for

x>0.

Solution:

(a)

Step 1:
Using the Quotient Rule, we have
$f'(x)={\frac {x^{\frac {4}{5}}((3x-5)(-x^{-2}+4x))'-(3x-5)(-x^{-2}+4x)(x^{\frac {4}{5}})'}{(x^{\frac {4}{5}})^{2}}}.$

Step 2:

(b)

Final Answer:
(a)
(b)

@@ Line 10: / Line 10: @@
 |'''1.''' Quotient Rule
 |-
-|'''2.''' Power Rule
+|'''2.''' Product Rule
+|-
+|'''3.''' Power Rule
 |}
@@ Line 20: / Line 22: @@
 !Step 1: &nbsp;
 |-
-|
+|Using the Quotient Rule, we have
 |-
-|
+|&nbsp; &nbsp; &nbsp; &nbsp; <math>f'(x)=\frac{x^{\frac{4}{5}}((3x-5)(-x^{-2}+4x))'-(3x-5)(-x^{-2}+4x)(x^{\frac{4}{5}})'}{(x^{\frac{4}{5}})^2}.</math>
 |}