9. y = Arccot“ Vx 2 Arccot Vx А. Arccot x С. Vx(1+x) x' +x* Arccot x В. Arccot x Vx(1-x) D. - - Vx(1+x) 10. y = Arcsin (e²^) 4x 4e А. 4x 4e 2x 2x 2e С. D. - В. 4x 1+e* 1+e** V1-e 4x 4x 11. y = 5 3 tn() 15' Inln 8 (3'# 5")_ А. С. Inln 15 (3'F 5^)_ 2Vx В. 15)(15*) D.

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

A:

Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: Solve for dy given xsin y - ycos x = 2 | dx sin y-ysin x А. cOS X-XCOs y sin y+ysin x В. coS X-XCOs…

A:

Q: 3) Estimate Y(2) using Euler's method with 0.5 long dY intervals. Y - 2X and Y(1) = 0. dx

A:

Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

A:

Q: Find the differential equation of the families of circles with center at (2, k) and with radius r.

A: Given,           The differential equation of the families of circles with center ar 2,k and with…

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

A:

Q: Find the differential equation characterizing the family of curves desonbed : 1. Careles passing…

A:

Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: first and second derrivative of: y=Arccos(e^2x)

A:

Q: Obtain the differential equation for the family of circles with center on the line x = 8.

A: The general equation for a circle can be written as

Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Sinh) esechct) dy

A:

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

A:

Q: differential equation of the family of circles whose center is on the line y = 3x

A: Please refer to the image below

Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

A:

Q: ① Solveing dy - - x dx = 。 ㅎ

A:

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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: Obtain the differential equation of the family of curves. 1. Circle with center at the origin.

A: The equation of a circle with center at (a , b) and radius r is given by (x-a)2+(y-b)2=r2 Hence…

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

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: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: Obtain the differential equation of the family of circle with center on the x-axis

A:

Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: Find the differential equation of the family of circles with center on x-axis.

A:

Q: 4- cosh x2 dy + (sinh x)y = e-* dx

A:

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

A:

Q: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

Q: Obtain the differential equation of all circles with center on line y = -x and passing through the…

A:

Q: y = Arctan ( sinh (2x)); y' = * O - 2 coshx /(1+ sinh^2 (2x)) O 2 coshx / (1+ sinh^2 (2x)) O 2/ cosh…

A:

Q: Parabolas with axis parallel to the y-axis

A: Equation of parabola parallel to y-axis and having center(h,k) and having distance a from vertex to…

Q: Circles with center on the line y = x

A:

Q: 4. Differentiate y with respect to x. y = (In Vcosh3x)(sinh(2x + 1) ex+1)

A: The given function is: y=lncosh (3x)sinh-1(2x+1)

Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

A:

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

A:

Q: Find the differential equation of the family of circles with fixed radius and tangent to the x axis.

A:

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

A:

Q: tan Зy limy 0 3y O 3 O undefined

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.