dy = 18yx³ dx and whose y-intercept is 4. y(x) =

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: y = 5x³

A:

Q: The equation of the tangent line to the curve at the given point. x² + y2 +3 = (2x+2y + 9x)2, (0, 1)…

A:

Q: Show that the slope dy/dx is defined at every point on the graph of 2y = x² + sin y.

A: Given- 2y=x2+sinx To prove- That the slope dydx is defined at every point on the graph of the above…

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5 =1

A: Product rule of differentiation:If f(x) is a function of u and v where both u and v are variables…

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: Use Bernoulli's Equation dy/dx=y-xy3e-2x

A:

Q: Find the equation of the tangent line to y = e-5t at t = 0. y =

A: Solution is given below:

Q: b. b. y = 2 1+e-x at (0,1)

A:

Q: Calculate dx/dy for the equation y4 + 1 = y2 + x2 and find the points on the graph where the tangent…

A:

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: Find an equation of the tangent line to the curve at the given point. y = Vx, (64, 8)

A:

Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

Q: ,4 Consider the curve whose equation is x4 + y* + 3xy = 5. The dy slope of the tangeant line, at the…

A:

Q: Figure 1 shows the graph of y4 + xy = x3 − x + 2. Find dy/dx at the two points on the graph with…

A:

Q: Find the exact length of the curve. y = ln (1 − x2),  0 ≤ x ≤ 1/3

A: We need to use the chain rule to find dy/dx.

Q: Find the equation of the tangent line drawn to the curve y4−4x4−6xy=0 at the point M(1,2).

A:

Q: Find the equation of the line tangent to the curve y = cos(2x) at the point where 3

A:

Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

A:

Q: Find an equation of the line tangent to the curve y = sin x atx = 0.

A: Solution -  Given equation -  y=sinx At x=0,  y=sin(0)=0 We have - x0, y0 = 0, 0   Equation for the…

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: A) Find the equation of the tangent line to the curve x²y + xy2 = 6 at x = 1

A: Given: The equation of curve , x2y +xy2 =6,  x = 6 To find: The equation of tangent line to the…

Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: Use implicit differentiation to find dy/dx and then d2y/dx2. Write the solutions in term of x and y…

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below

A: Given,

Q: = y² dy dx

A:

Q: (b) Find the equation of the line normal to the tangent at the point x’y+xy² = 6.

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5=1

A: Differentiate the given equation with respect to x.

Q: Determine an equation of the tangent line to y= (e3x+2)5 at the point (0 , 243) then solve it for y.

A: We have to find the value of y.

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x4-3xy2=2

A: We have to find dy/dx of curve equation .Curve equation is given by:

Q: find the values of the derivatives

A: given that, y=1-1xand we have to find dydx at x=3

Q: Find for the curve dx In (2x) + 5xy + y = 3.

A:

Q: Find dy/dx for the curve x2y3 - 2xy = 6x2 + 2y3 +1

A: The given curve,    x2y3-2xy=6x2+2y3+1

Q: 1. find dy/dx of each equation using implicit differentiation. a. x2 - y2 = 9 b. 3x2 - y3 -3xy = 0

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule; f·g'=f'·g+f·g'   Given: (a). x2-y2=9

Q: Find the length of the curve y = ln (1 - x2), 0<=x<=1/2

A: Given:

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

A:

Q: Consider the curve given by y2 + (1+x³)3 = xy + 8. Find the equation of the tangent line to the…

A: To find the equation of line tangent to the given curve at point (1,1)

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 the PS of (16x+5y)dx +(3x+y)dy= 0. if the curve to pass thru the point (1,-3

A: 16x+5ydx+3x+ydy=0 -1equation 1 can be written as

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −4x2 −3x−1=y2 −y

A: The given function is,

Q: Find an equation for the tangent to the curve at y =x2 + 1, (4, 17) y = -4x - 15 O y = -8x - 15 y =…

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x3+y4=3

A:

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Consider the curve given by y2 + (1+x³)³ = xy + 10. Find the equation of the tangent line to the…

A: Considering the curve- y2+1+x33=xy+10 Firstly, find the slope of the curve. dy/dx is the slope of…

Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: Find the equation of the tangent to the curve y = x+2x3 through point ( 8,12 ). a. 7x – 6y + 14 = 0…

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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: Find

A: