Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin
The equations are both the same with a slope of 2 and y-intercept of 3.
<h3>Solution to system of equation</h3>
A line is the distance between two points. Given the equations below;
2y - 4x = 6
y = 2x + 3
___________
y - 2x = 3
y = 2x + 3
The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.
Learn more on equation of a line here: brainly.com/question/13763238
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Step-by-step explanation:
This leads to another rule for exponents—the Power Rule for Exponents. To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, (23)5 = 215. For any positive number x and integers a and b: (xa)b= xa· b.
Answer:
2^1
Answer: y = 5x + 13
<u>Step-by-step explanation:</u>
Parallel means it has the same slope.
Given line y = 5x + 5 --> the slope is 5, so parallel slope is 5
Use the Point-Slope formula: y - y₁ = m(x - x₁) such that
y + 2 = 5(x + 3) <em>input m and (x₁, y₁) into the Point-Slope formula</em>
y + 2 = 5x + 15 <em>distributed</em>
y = 5x + 13 <em>subtracted 2 from both sides</em>