You could do the question the way it is written, but it is far easier to bring the negative power up to the numerator.
y= x^2 - 3. The derivative of that is
dy/dx = 2x The three is a constant and is always dropped when a derivative is taken
d(-3)/dx = 0
If you are a purist and want to solve the question the way it is written, you could do it this way.
dy/dx = d(1)/dx x^-2 - d(x^-2)/dx * 1
======================
(x^-2)^2
dy/dx = - (-2 x^ - 3) / x^-4
dy/dx = 2 x^-3 * x^4
dy/dx = 2 x^(-3 + 4)
dy/dx = 2x ^ 1
dy/dx = 2x <<<<< answer
By using the information given on the graph, we can see that a = 3.
<h3>
How to find the value of a?</h3>
Here we have an exponential of the form:
And by looking at the graph, it passes through (0, 4) and (2, 36), so we can write:
From the first equation we get that p = 4, replacing that on the second one we get:
So we conclude that a = 3.
If you want to learn more about exponential equations:
brainly.com/question/11832081
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Folded mountain with waves, twists, and turns. I believe because the article stated it was gradual and various patterns were formed.
Answer:
- The general solution is
- The error in the approximations to y(0.2), y(0.6), and y(1):
Step-by-step explanation:
<em>Point a:</em>
The Euler's method states that:
where
We have that , , ,
- We need to find for , when , using the Euler's method.
So you need to:
- We need to find for , when , using the Euler's method.
So you need to:
The Euler's Method is detailed in the following table.
<em>Point b:</em>
To find the general solution of you need to:
Rewrite in the form of a first order separable ODE:
Integrate each side:
We know the initial condition y(0) = 3, we are going to use it to find the value of
So we have:
Solving for <em>y</em> we get:
<em>Point c:</em>
To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:
Find the values y(0.2), y(0.6), and y(1) using
Next, where are from the table.