What is the formula for the slope dy/dx of a parametrized curve x = ƒ(t), y = g(t)? When does the formula apply? When can you expect to be able to find d2y/dx2 as well? Give examples.

Q: Find the exact length of the curve. y = ln(Sec x),   0≤ x ≤ π/4

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Q: Find the equation of the tangent line to the curve (piriform) y^2 =x^3(7-x) at the point (1,√6) a…

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Q: Determine the equation of one of the curves for dy/dx = 4x which passes through the point (2, 3).…

A: We need to find a curve for dydx=4x which passes through 2,3.

Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t3/2 at t = 1. Also…

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Q: dy Then find the slope of the curve at the given point. dx Differentiate implicitly to find…

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Q: se implicit differentiaion to find dy/dx for the curve below. 1. xy3 + 4x2 = tan y2 + 3

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Q: Find the derivative dy/dx of the hyperbolic spiral r=aθ.

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Q: Find y in terms of x. dy dx (32-x) curve passes through (2,2)

A: According to question, given differential equation, dydx = x4 32-x57

Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

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Q: Find the equation of the tangent to the curve given by x=t cos⁡t, y=t sin⁡t, at t=π. (HINT: Find…

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Q: Find the length of the curve y2 = ln x, -1 ≤ y ≤ 1.

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Q: Find the second derivative of the parametric equation ; x = t3 + 1, y = 4t2 −4t.

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Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

A: x = t2 + 1 y = et - 1 dy/dx = dy/dt ÷ dx/dt

Q: • What restriction (on x or y) does dy have? What dx point (x, y) does this correspond to? • Find…

A: According to our policies we are allowed to answer only one question at a time. If you want solution…

Q: I need help with these two questions please take show steps so that I may understand.

A: 5) a) The function is

Q: Differentiate implicitly to find dy/dx.

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Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: What is the equation of the curve whose tangent line passes through the point sec (In x) dx? (1,2)…

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Q: 2. Calculate the derivative dy for the parametric equation x = t² + ³ + ln(4t+1), y=e5t² giving your…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: Find an equation of the tangent line of y = e" cos T, at z= 0.

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Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: dy for the curve x = yª. dx Find

A: First take log both sides than use lograthim derivative.

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: Find the derivative dy/dx of the cardioid given by the equation r=f(θ)=a(1+cosθ).

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Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: 29. Differentiate the following implicitly to find dy/dx. Then find the slope of the curve at (1,…

A: Given: x3+y3=9 To Find: Differentiate the following implicitly to find dydx.Slope of the curve at…

Q: (d) The curve with equation 2 (x² + y²)² = 25 ( dy (i) Examine by using implicit differ dx Determine…

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Q: Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point. y2 8;…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the equation of a curve having a slop by dy xy? у 3 ху? —, x > 0 dx and passing through the…

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Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: (a) Find the equation of the tangent line to the curve x = e', y=e %3D at t = 1 without eliminating…

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Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: A curve is defined implicitly by the equation x²+xy+y? =1 dy Differentiate implicitly to find dx

A: here we use basic differentiation form.

Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…

A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3   Apply the chain…

Q: A curve is defined implicitly by the equation x² + 3xy + y² = 1 Differentiate implicitly to find dy…

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Q: A curve is defined implicitly by the equation x²+xy+y³=1 dy Differentiate implicitly to find dx

A: Follow the procedure given below.

Q: Find an equation of the tangent line to the curve at the following point: y = z°e², (1,1/e) y =

A: SOLUTION-

Q: A girl is sliding down a slide shaped like the curve y = 3e-*/3, Her y-coordinate is changing at the…

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Q: use implicit differentation to find dy/dx and d2y/dx2 at the point (1,0) for the given function…

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Q: Find the value of dy/dx at the point (−2, 1) for the function which is defined implicitly by

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Q: xys = 1 at (1, –1). Find the slope of the tangent to the curve dy dx \(1,–1)

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Q: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: 2 Calculate the (d^n*y)/(dx^n) derivative of the curve with the parametric equation x=lnt, y=t^alpha

A: The given problem is to find the nth derivative of y with respect to x of the given parametric…

Q: Consider the curve whose equation is x4 + y + 3xy = 5. The dy slope of the tangeant line, at the…

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Q: Calculate the derivative dy for the parametric equation x=t7+t³+ln(5t + 1), y = e4t²_ +t6 giving…

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Q: d. Try to find dx dy at (0, 0) on both graphs. What goes wrong? How does this relate to their…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.