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
-10d^2 + 11d - 2
To find this, distribute the - to 7d^2 - d - 6.
This will give you a new equation of:
-3d^2 + 10d - 8 -7d^2 + d + 6
Combine like terms to get the answer above.
Hope this helps!
Answer:
- principal: $7000
- interest rate: 3%
Step-by-step explanation:
amount repaid = principal + interest
$7840 = principal + $840
$7000 = principal . . . . . . . . subtract $840 from both sides of the equation
___
I = Prt
840 = 7000·r·4
840/(4·7000) = r = 0.03 = 3%
The principal was $7000; the interest rate was 3%.
Answer:
C
Step-by-step explanation:
c. y = 2x + 3
first you need to find the y-intercept which is 3
and then the slope rise/run which is 2 so y = 2x + 3
