Answer:
Step-by-step explanation:
<u>The Derivative of a Function</u>
The derivative of f, also known as the instantaneous rate of change, or the slope of the tangent line to the graph of f, can be computed by the definition formula
There are tables where the derivative of all known functions are provided for an easy calculation of specific functions.
The derivative of the inverse tangent is given as
Where u is a function of x as provided:
If we set
Then
Taking the derivative of y
![y'=3[tan^{-1}(x+\sqrt{1+x^2})]'](https://tex.z-dn.net/?f=y%27%3D3%5Btan%5E%7B-1%7D%28x%2B%5Csqrt%7B1%2Bx%5E2%7D%29%5D%27)
Using the change of variables
![\displaystyle y'=3[tan^{-1}u]'=3\frac{u'}{1+u^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%3D3%5Btan%5E%7B-1%7Du%5D%27%3D3%5Cfrac%7Bu%27%7D%7B1%2Bu%5E2%7D)
Operating
Answer:
$105 interest
Step-by-step explanation:
Interest = $105
Hello :
<span>the parabola's equation is : f(x) = a(x+3)²-1
</span><span>the coefficient of the squared expression in the parabola's equation is : a
but ; f(4) = 0
0 = a(4+3)²-1
49a-1=0.....a=1/49
f(x) = 1/49(x-3)²-2</span>
16)
s^1/4 * s^1/4 * s^1/4 * s^1/4 = s^(1/4 + 1/4+1/4+1/4) = s^4/4 = s
Answer is s
15) Answer is 1. (because any number to the 0 exponent is equal 1 , except 0)
17)
= (t^3/6)^2 = t^6/6 = t
Answer is t
Answer:
The answer is 121
Step-by-step explanation:
So basically it's like dividing 4 from 4 and you get 1
Then 8 from 4 and it would come out as 2
And divide 4 once more from 4 and get 1 again
4÷4=1
8÷4=2
4÷4=1
Then out the answers together and you got 121
