Consider the implicit relation yx +1= 7y. In the box below, solve the equation for y as a function of x.

Q: Find the relative extremes of the two-variable function f(x, y) = 2x3 + 2y3 + 6xy + 1

A:

Q: Find b, if the function f(t) = t?.

A: This is a Fourier analysis question. Lets solve it.

Q: Find and simplify the function values. f(x, y) = 8x + y2 Exercise (a) f(x + Дх, у) — f(x, у) Дх

A:

Q: Find of the function x³ z2 – 5æyz = a? + y %3D

A:

Q: Find f'(0) for the function f (x) = 3.xe 5x %3D Answer:

A: use the formula for the derivative  d ( u v ) = u dv + v du  ddxeax=aeax,ddxax=a

Q: find the specific function values. ƒ(x, y) = x2 + xy6 ƒ(-3, -2)

A: Given function:

Q: Find the domain and range of this relation { (x, y) RxR: V+3}?

A: Given query is to find the domain and range ofbthe relation.

Q: t(x, y) x² + y?

A:

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

A:

Q: Find y for the function y = ( secx x2 5

A:

Q: Determine whether the equation xy - 5y = 1 defines y as a function of x.

A: Here we determine whether the equation xy-5y=1 defined y as a function of x.

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

A:

Q: If f is a function defined by the equation y = f1x2, then x iscalled the variable, and y is…

A: Given: If f is a function defined by the equation y = f(x), then x is called the _________ variable,…

Q: Given the function f(x) = x(x – 3)(x + 2), find 1) its y-intercept: 2) its x-intercepts: 3) As x →…

A:

Q: find the specific function values. ƒ(x, y) = x2 + xy5 ƒ(2, 3)

A:

Q: Sketch the graph of the function. f(x, v) = y? + 7

A:

Q: eliminate the parameter to find an explicit equation for y as a function of x.  x=4 - 2t, y=5 + 3t

A: x=4-2t x+2t=4 2t=4-x t=0.5(4-x)

Q: Find all possible functions with the given derivatives. a. y'=7x^6 b. y'= 7x^6 c. y'=8x^7-7x^6-7

A:

Q: Consider the function y = 1 2r2

A: To find: The horizontal and vertical asymptotes of fx. Given: The function is fx=2xx2-1. Concept…

Q: Find the domain and range of f(x,y) = e* + /y + 2

A: We can find the answer given below

Q: Use C to represent the arbitrary constant. y =

A:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x    . e…

A: Derivative of a function is the rate of change of function with respect to another variable.…

Q: Determine whether the equation defines y as a function of x. x =  |3y|

A: Given,           x =  |3y|

Q: Find the function g(x) which is obtained by reflecting the graph of f(x) about y axis and moving 2…

A: solution

Q: . Write a rule for a linear function y = h(x), given that h(1) = 6 and h(-3) = 2.

A: Our Aim is to write a rule for a linear function y=h(x), given thath(1)=6 and h(-3)=2

Q: If 10x³y* + e*Y = 5 defines y implicitly as a function of x, find y.

A: Using derivatives of implicit function.

Q: For what values of  r does the function satisfy the y =  e rxequation  y"  + 6 y'   + 8y  =0?

A: Given function y=erx To find value of r which satisfy the equation y"+6y'+8y=0 Solution:…

Q: find all possible functions with the givenderivative. y' = 2x - 1

A: Given y'=2x-1 that is  dydx=2x-1 Integrating with respect to x, ⇒y=x2-x+C Where C is the constant of…

Q: Find the relative extremes of the two-variable function f(x,y) = 2x3+2y3+6xy+1

A: maximum at (-1,-1)

Q: Find dz implicitly of the relation r + y³ = 3ry.

A:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x.…

A: To find: Derivative of yy+1 with respect to x, assuming that y is implicitly a function of x.

Q: ) Find of the implicit function a? + 5xy + y? – 2x + y – 6 = 0 at the point 1. . (1, 1).

A: Topic:- derivatives

Q: Differentiate the function. f(t) = 7 - 글

A: We have to differentiate of the  function

Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A:

Q: From now on consider the function f(x, y) = e$n(x) y.

A: direction of fastest increase is along the gradient vector  Given f(x,y)=esinx y

Q: y = x"ex

A: To graph the curve

Q: Differentiate the function with respect to the independent variable. f(x) = - 8x+ e + e f'(x) = D

A:

Q: Find , where y is defined as a function of x implicitly by the equation below. dz' 2y5 - 2ry = -2…

A:

Q: 2. y Insin(x-A) +B; y″ + (y')² +1=0

A: What is Differential Equation A differential equation is an equation that involves the derivatives…

Q: Given the function + y-4, find y'. Oy = Oy =

A:

Q: Use the graph of f(x) = [[x]] to graph the indicated function. y = [[2x]]

A: Given function is: y=[[2x]] It is greatest integer function. Given basic function is: fx=[[x]]

Q: Sketch the level curve of the function f(x, y) = x² + y? 2 for c = 1.

A: Level curve:  The level curves of a function f of two variables are the curves with equations f (x,…

Q: Differentiate the function with respect to the independent variable. h(t) = t - 7t+2 h'(t) =O

A: Given function, h(t)=92t2-7t+2

Q: Solve for y in terms of x for the foltowing

A: e(ln2)y=12lne(ln2)y=ln12yln2=-ln2y=-1

Q: Find constants cq and c2 such that the function y(x) cje + c2e° satisfies y(0) = 1, and y' (0) =…

A: The values of constants c1 and c2 of the giben general solution of differential equation satifying…

Q: The function f(x,y)=/26-2x²-y² is continuou at point (2,-3). .A False .B True

A: Givenfx,y=26-x2-y2

Q: Find y' if 3x2- (ry?) = 2y.

A: Given that, 3x2-xy212=2y3 Find the derivative of the given equation.

Q: Given the equation 3x + 2xy -y = 0, evaluate Assume that the equation implicitly defines y as a…

A: We have to find the derivative dydx of the given function.     According to our guidelines, we can…

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.