Find the equation of the tangent line to the curvef (x) = -x' + 2x at x = 1. о Тx) 3D 1 + (-1)(х — 1) o T(x) = 2 – 1(x – 1) O T(x) = 1 + 2(x – 1) o T(x) = 1(x – 1) -

Q: Determine the equation of the tangent line for y = sech(In x) + tan-(x²) tangent at x = e*. A. Yr =…

A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

A:

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

A:

Q: Consider the differential equation, x' = f(x), vith f(x) = { 1 - x x > Compute the solution to the…

A: Given, y'=fx fx=x,x<121-x,x≥12

Q: Obtain the general solution of the second order ordinary differential equa- tion y" +y= sec"(1)

A:

Q: If z = +3y, find the differential dz. dz =

A:

Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

A:

Q: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: Find the 4th order differential of the function y=√2x+1.

A:

Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux  &  vx are the differential functions of x. To differentiate these type of…

Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

A:

Q: D. Solve the differential equation using Loaplace transform of y" + y = 6sin 2t ; when y(0) = 3 and…

A:

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

A:

Q: 2. Find dy/dx by implicit differentiation: 5x^2y+5y^2x=-3

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

A:

Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

A:

Q: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

A:

Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: Compute the differential dy  for  y=(6x+sinx)^3

A:

Q: -Solve Bessel's Equation of order zero point x = 0 + xy = 0 around

A:

Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

A:

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

A:

Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

A:

Q: Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to…

A:

Q: Find the equivalent differential equation for all tangent lines of the parabola y = x^2

A:

Q: tan(4x + 8). Find the differential dy when x = Let y 1 and dæx 0.3 Find the differential dy when x =…

A: In the given question we have to find dy of the function at both of the given value.

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

A: The given data is: N=74x-x2 To use differential approximation to estimate the increase in sales that…

Q: Find the slope of the tangent line to the graph of f(x) = x· 2e*cos-1t dt at x = 1 Jln x

A:

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

A:

Q: Repeat Exercise 60, except with these derivative boundary conditions: y'(0) = 0, y'(π) = 1. In part…

A:

Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

A:

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

A:

Q: Approximate Ay using differentials for y = x2 - 4x at x = 6 when Ax dx = 0.03.

A: