Dy/dx = x y, on the region 3 ≤ x ≤ 6, and 6 ≤ y ≤ 3 Don't cheat!PROBLEM 1 Find the length of the graph for $ y = 3x2 $ on the closed interval $ 1 \le x \le 2 $ Click HERE to see a detailed solution to problem 1 PROBLEM 2 Find the length of the graph for $ y = x^{3/2} $ on the closed interval $ 0 \le x \le 4 $ Click HERE to see a detailed solution to problem 2To see this consider the example of the function y = x4 A graph of this function is shown in Figure 3 There is clearly a minimum point when x = 0 But dy dx = 4x3 and this is clearly zero when x = 0 Differentiating again d2y dx2 = 12x2 which is also zero when x = 0 O Figure 3 The function y = x4 has a minimum at the origin where x = 0
Consider The Autonomous First Order Differential Equation Math Dy Dx Y Y 3 Math And The Initial Condition Math Y 0 Y 0 Math By Hand Sketch The Graph Of A Typical Solution Math Y X Math When Math Y 0 Math Has The
Dy/dx=y/x graph
Dy/dx=y/x graph-The solution curves are hiding in the slope field Given one point of the particular solution curve, you can sketch the graph from that point, in both directions, to see the graph of the solution The initial value problem 342 dy x dx with y = – 1 when x = 0 is shown Notice howYes, as it is in the form dy dx P (x)y = Q (x) where P (x) = − 1 x and Q (x) = 1 So let's follow the steps Step 1 Substitute y = uv, and dy dx = u dv dx v du dx So this dy dx − y x = 1 Becomes this u dv dx v du dx − uv x = 1 Step 2 Factor the parts involving v Factor v u dv dx v ( du dx − u x



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1 dy/dx = x The applet shows the slope field for dy/dx = x We know that the general solution to this differential equation is y = ½x² C and one of this family is shown in magenta You can clickdrag the magenta point to move the solution to other members of the family The gray line segments in the background of the graph represent the slope fieldDy x dx y x dy e dx (2 ) dy yy dx What Do Slope Fields Show You?Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutor
The slopes at several points on the graph are shown below the graph y x dy dx 2x 3y2 2y 5 dy dx 3y2 2y 5 dy dx 3y2 2y 5 2x dy dx 3y2 dy dx 2y dy dx 5 dy dx 2x dy dx 3 y2 dy dx 2y dy dx 5 dy dx 2x 0 d dx y3 d dx y2 d dx 5y d dx x2 d dx 4 d dx y3 y2 5y x2 d dx 4 x dy dx y3 y2 5y x2 4 dy dx x y 25 Implicit Differentiation 141Geometry of 2x2 Matrix Multiplication with Intro QuestionsExample 4 The graph of $$8x^3e^{y^2} = 3$$ is shown below Find $$\displaystyle \frac{dy}{dx}$$ Step 1 Notice that the lefthand side is a product, so we will need to use the the product ruleIdentify the factors that make up the lefthand side
Here I introduce differentiation, dy/dx as used in calculus See the playlist on differentiation at https//wwwyoutubecom/playlist?list=PL5pdglZEO3NjDXt9xD/dx x^2 y^4, d/dy x^2 y^4 Extended Keyboard; So dy/dx literally means how the variable y changes as x changes Imagine a graph, draw the line y = 1 It doesn't matter what value of x you look at, y = 1 It x changes, decreases or increaes, y will always be 1 won't it So dy/dx = 0 because no matter how x changes, y



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Compute the Area of the Surface of Revolution formed by revolving this graph about the y axis Solution First solve the equation for x getting x = y 1 / 2 Here is a carefully labeled sketch of the graph with a radius r marked together with y on the yThe graph of dy/dx a) Find the explicit expression for the original function y=f(x) on the interval 2 € (3,1) b) f(3) A/ c)f(1) = A d) Sketch the graph of the function y=f(x) Clearly label and scale the axes Previous question Next question Get more help from Chegg How do you solve the differential equation #(dy)/dx=e^(yx)sec(y)(1x^2)#, where #y(0)=0# ?



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Taking dx/dx of a function is not a thing as that simply equals 1 You always take the derivative with respect to x of both sides in an implicit relation Then you use the chain rule to simplify After that, you bring all the dy/dx terms to one side and the other terms to the other side and then simply solve for dy/dxAssuming that you did the exercise correctly, you should have produced a picture that was simply a larger version of the following Slope Field for dy/dxHere are some brief observations from the graph above Original function y = 05x² – x – 15 Derived function dy/dx = x – 1 For 'x' values less than x=1, the original function (blue) is decreasing left to right, so all tangent lines will have a negative gradient



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Slope Fields With Mathematica Exercise C 2
y = x 1 C/e^x dy/dx=xy not separable, not exact, so set it up for an integrating factor dy/dx y =x the IF is e^(int dx) = e^x so e^x dy/dx e^x y =xe^x or d/dx (e^x y) =xe^x so e^x y = int xe^x \\ dx qquad triangle for the integration, we use IBP int u v' = uv int u' v u = x, u' = 1 v' = e^x, v = e^x implies x e^x int e^x \\ dx = x e^x e^x C so going back to triangle e^x y = xThe way of solving such differential equations is pretty straightforward (d2y)/ (dx2)5 (dy/dx)6y=0 One solution was found y = 0 Step by step solution Step 1 y Simplify — d Equation at the end of step 1 ( (d2)•y) y (———————— (5• ( (d•—)•x)))6y =The function of the first degree y = mx always represents a line passing through the origin of the axes m is called angular coefficient If m > 0 the function is increasing if m < 0 the function is decreasing if m = 0, the line coincides with the axis of X > y = 0




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Slope Fields With Mathematica Exercise C 4
Step 3 Calculate the "y" coordinates by filling the "x" coordinates in to the function Step 4 Calculate "dx" and "dy" with subtraction Step 5 Divide "dy" by "dx" 6 Summary To find the derivative of a function, you have to divide the change in "y" (dy) by the change in "x" (dx)Explain the strategies Martin Luther King Jr uses to develop his ideas in The equation y = xc tells you nothing because c can take any value It is literally as useful as saying 0 = 0 It doesn't make any sense to manipulate dy/dx = y/x in the first place if you understand what that equation actually means, and this tutorial does not explain that to the reader




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