dy d’y dx’ dx² 17. Find and find the slope and concavity (if possible) at the given value of the parameter t. x=t+1, y=t² +3t, t = -2

Q: Find dy| dx| and d2 y| dx2 . For which values of t is the curve concave upward? 15. x=t-1n t, y=t+1n…

A: x=t-ln ty=t+ln t

Q: Find dy/dx. x = t sin(t),    y = t2 + 6t

A: given ,        x = t sint        y = t2 + 6t

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

A:

Q: Given that dy =0 dx when x=2 for the curve y=x³ - 2x2– 4x d?y and hence find which of the following…

A: We have to find the solution.

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

A:

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

A:

Q: dy Find dx for the curve: x = t, y= 2/t, t>0

A:

Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: dy by differentiating implicitly. Do not subs da (a) Find dy dx (b) Solve the equation for y as a…

A: We will find the derivative.

Q: Can you please solve these two sub problems and show all of the steps and say the correct letter

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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: dy/dx The DE yet describes the slope of some curve y=f (x) in the xy-plane at every point (x,y)…

A:

Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…

A: Differentiating with respect to x, we get

Q: Given that dy =0 dx when x=1 for the curve y=x³+3x2 – 9x +6 d²y and hence find which of the…

A: y=x3+3x2-9x+6 we have to find out d2ydx2 at x=1

Q: Find dy/ dx and d2 y/dx2. For which values of t is the curve concave upward? x = et, y = te-t

A:

Q: :a stream function is given by: Y=2x²y + (x+t)y2 Find the velocity equation for flu me = 1s?

A:

Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

A:

Q: Find  dy dx at the value of the parameter. x =    t,  y = 2t + 8,  t = 16

A: See attached file for a step by step explanation.

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

A:

Q: Find dy/dx and d2 y/dx2 . For which values of t is the curve concave upward? 13. x = et , y = te-t

A:

Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: 5.) Find and d²y , and find the slope and concavity(if possible) at the given value of the dx2 dx…

A: Given Find out the derivative dy/dx using formula

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

A:

Q: dy Find for the functions x = a(cost + tsint) , dx y = a(sint – tcost)

A:

Q: Include the plots of the solutions for y(x) and its derivative! d²y 34 + 2y = 0, initial condition:…

A:

Q: Find dy/dx and d²y/dx². x = et, y = te¬t dy dx dzy dx2 For which values of t is the curve concave…

A: We have to find derivative

Q: Find dy/dx and d?y/dx2². x = t2 + 1, y = t2 + 5t (2t +5) dy dx 2t (2:(2) – (2t + 5)(2)) d²y dx2 412…

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Q: dy If x = t – sin t and y =1- cost, then find at t = %3D dx a. -2 b. 0 С. 1 d. 2

A:

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

A:

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

A:

Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

A:

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward? x = t2 + 1, y = et – 1

A: x=t2+1y=et-1

Q: dy 11) Find where x and dx y are related by the equation xsin(y) – ycos() = 0.005. %3D

A: We use product rule for both terms

Q: Find f(x) if y = f(x) satisfies dy = 91ya"2 dx and the y-intercept of the curve y = f(x) is 5.

A:

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: Find 4 at the point t = 5. dy dx c(t) = (t^, t³ – 3) dy dx (at t = 5) = ||

A:

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: Find dy/dx and d²y/dx². х %3еt, у3 te-t dy dx dzy dx2 For which values of t is the curve concave…

A: Given

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 dy/dx and d2y/dx2. x = cos(2t),    y = cos(t),    0 &lt; t &lt; π   For which values of t is…

A:

Q: dy Find at the origin on the curve: - dx x² + y + x + 3y 0

A:

Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: 2) Given: x = t³ + 1, y = t² – t a) Find dy/dx and d²y/dx². b) For which values of t is the curve…

A: The given functions are: x=t3+1, y=t2-t

Q: Find [(dy)/(dx)] if the curve is defined by 7 x² e7 Y + 6 y2 e2 x = 16. %3D [(dy)/(dx)]

A: Given:     7x2 e7y + 6y2e2x = 16

Q: Find dy/dx and d2y/dx2 at the given point without eliminating the parameter. x=1/2t2+9  y=1/3t3+4t,…

A: We have, x=12t2+9, y=13t3+4t, and t=2 Now, differentiating x=12t2+9 with respect to t, we get the…

Q: dy If y=t+t and x= 5t+7 then at x = 17 is: dx

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Q: For the curve y 2 + xy = 1 determine the value of: dy d²y dx(0,1) dx²

A:

Q: dy lat dy %3D dx dt 5) Find the equation of the line tangent to the curve using the fact that: For…

A: Given equation is Differentiating with respect to , we get   Now, Now, t=e corresponds to given…

Q: ay 13) Given X = e', y=t e. Find dx and d²y dx? . For which values of t is the curve concave upward?

A:

Q: given the curve x^3+2y=y^2 A. use i mpliciit differentiation to find dy/dx B. find the slope of…

A: Consider the given equation x3+2y=y2. A. Obtain the implicit differentiation as follows.…