2.8.1

By definition of the derivative,

We have

and

Combine these fractions into one with a common denominator:

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

3.1.1.
![f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%5E5%20-%20%5Cdfrac1%7B4x%5E2%7D%20%2B%20%5Csqrt%5B3%5D%7Bx%7D%20-%20%5Cpi%5E2%20%2B%2010e%5E3)
Differentiate one term at a time:
• power rule


![\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}](https://tex.z-dn.net/?f=%5Cleft%28%5Csqrt%5B3%5D%7Bx%7D%5Cright%29%27%20%3D%20%5Cleft%28x%5E%7B1%2F3%7D%5Cright%29%27%20%3D%20%5Cdfrac13%20x%5E%7B-2%2F3%7D%20%3D%20%5Cdfrac1%7B3x%5E%7B2%2F3%7D%7D)
The last two terms are constant, so their derivatives are both zero.
So you end up with

6.75 is the answer to your question
Answer:a gallon
Step-by-step explanation:if you add cup by cup you can see that it is a gallon by adding them or putting it in a allon jug
Answer:
B
Step-by-step explanation:
I had this question a few months back and I think this was the answer not too sure though
Answer:
x = 9.5
Step-by-step explanation:
Given
=
( cross- multiply )
3(4x - 6) = 4(2x + 5) ← distribute parenthesis on both sides
12x - 18 = 8x + 20 ( subtract 8x from both sides )
4x - 18 = 20 ( add 18 to both sides )
4x = 38 ( divide both sides by 4 )
x =
= 9.5