Consider the curve given by the equation y^3−y=x^2+ 3x. (a) Find dy/dx. (b) Find the equation of the tangent line to the curve at the point (0,1). Write your answer in slope-intercept form.

Q: Find the equation of the tangent line to the curve y = 8 ln(x – 63) at the point (4,0). y =

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Q: Find an equation of the tangent line at the point indicated. y = ln(sinx),      x = π /4

A: The equation of a tangent line can be calculated using the slope point form of the equation of line.…

Q: Determine the equation of tangent line to the curve of the equation 3xy^2-x^2y=5x-3 at (1,1)

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Q: Differentiate (x-2)2+(y-3)2=9 at (7/2, ((6+3√3)/2)). Then use it to determine the equation of the…

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Q: What is the slope of the line tangent to the graph of y=tan 1(-2x) at x = 2? The slope of the…

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Q: Determine the equation of the tangent line for the graph y 4 sin z + 6x at x = keep every number in…

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Q: Find the slope of the tangent line to the curve 3a? – 4xy – ly3 = - 84 at the point (2, 4).

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Q: Find an equation of tangent line at the point (−1, 1) to the curve x^4y^2 + 1 = x^2 + y^3

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: What is the equation of the tangent line to the curve at the point (1, 2) The equation of the curve…

A: The given curve y3-xy2=4 at the point (1,2)

Q: Find an equation of the tangent line to the curve at the given point. у %3D sec(x), (л/3, 2) 2nv3 y…

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Q: Find an equation of the tangent line to the curve  y = x sq root of x  that is parallel to the line…

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Q: Find an equation of the tangent line to the curve y = 5 – 2x – 3x² at (1,0). y =

A: We will find the equation of the tangent line to the curve at the given point as following.

Q: 2 at the point ( 2, 1 Find an equation of the tangent line to the graph of y = e y =

A: we have to find the equation of the tangent line to the given function. We know that slope of the…

Q: What is the equation of the tangent line to the curve y= In(x“ + 1) at x=1?

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Q: Find an equation of the tangent line to the curve at the following point:  y=4/1+e^-x, (0,2) y=?

A: We first find the slope of the tangent using the first derivative y=41+e-xy=4(1+e-x)-1…

Q: Find an equation of the line tangent to the curve defined by " + 5xy +y = 68 point (2, 2) at the

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Q: Find the tangent equation to the curve y = sin² x at point x = 3.

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Q: Find the equation of tangent and normal lines to the curve xs sin(2y) = y cos(2x) at the ㅠ ㅠ point…

A: Solution of this question is

Q: How do you find the equation of the tangent line of xy = 36?

A: We have to discuss How do we find the equation of the tangent line of xy = 36.

Q: Find the equation of tangent line to the curve y=ln(2x+3) at x=2

A: y=ln2x+3 at x=2. Differentiating with respect to x, we get dydx=12x+3·d2x+3dx=12x+3·21+0=22x+3 Now…

Q: Determine the equation of the line tangent to x² + sin y = xy² +1 at the point (1,0).

A: The equation x2+siny=xy2+1, we have to determine the line of the tangent at the point (1,0).

Q: Find the slope of the line tangent to the curve x + sin(y+π) = 2x3 + ey at the point (-1,0). Show…

A: Topic:- application of derivatives

Q: Find the equation of the tangent line to the curve y = rVI at the point (4, 8). %3D

A: We have to find the equation of tangent

Q: For the curve 3e arcsin (y) + 2 (x² + y²) = 2, find the slope of the tangent line at the point…

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Q: Find the equation of the tangent line to the curve y = 3x2 – x at the point (1,2). y =

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Q: Determine the equation of the tangent line to the curve, y = 4x e at x = 1. Use exact values.

A: Given y=e4xx3     at x=1To find equation of tangent:

Q: Find the equation of the tangent line to the curve y = 8/x2 + x + 2 at x = 2.

A: Given, y=8x2+x+2,  at x=2 slope of curve at x=2 is dydx dydxx=2=-82x+1x2+x+22dydx=-4064=-5/8 at x=2,…

Q: Find the slope of the tangent to the curve y= 2 sin'x at x-

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Q: Find the equation of the tangent line to the curve y = 4r- 3r through the point r= 2 using the…

A: Given curvey=4x-3x2

Q: Find the equation for the tangent line to the curve y = 25 X + x² at x = 5.

A: Equation of tangent line to a curve y=f(x)  at x=a is given by y-f(a)=f'(a)(x-a)

Q: Find the equation of the tangent line to the curve y=xVx +5 at the point (2,6).

A: Given : y= x √(x²+5)  To find tangent line equation, we need to find differentiation of this…

Q: Find the slope of the tangent line to the curve 2² – -1 4.xy + 4y: at the point (1, - 1),

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Q: What is the slope of the tangent line to the curve y= -sin 3x at x=

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Q: find the equation of a tangent line for y=arcsin(x/8) at the point (4,π/6)

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Q: Find the equation of tangent line of function ²+ arctan y = y-1 at point(-t, 1).

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Q: The equation of the tangent line to the curve: y + 5 = 2x at x = 5.

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Q: At what point on the curve y = sinh x does the tangent line have a slope of 1?

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Q: How can we find the slope of the tangent line to the parabola y = x2 at the point?

A: Consider the following equation of parabola: y=x2 Differentiate y with respect to x: dydx=ddxx2=2x

Q: Find an equation of the tangent line to y = 5 sin(x) at x 4

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Q: Find the equation of the tangent line to the function y = sec'x at the point :2 4-

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Q: Find the equation of the tangent line to the curve x = 1 - cose, y = 0 -sin0 at 0= 4 -

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Q: Determine an equation of the tangent line to the curve y = (3x)(sinx) at x =

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Q: Find the equation of a tangent line of y = sin(x + π) at the point π/6.

A: We find dy/dx first  Then we plug x=π/6 to find the slope of the tangent.

Q: Find the equation of the tangent line to the curve 2 2 1= V sinx+x² at the point %3D (IT,"),

A: SOLUTION-

Q: Find the equation of the tangent line to the curve y = In(x³ – 26) at the point (3, 0). Tangent Line…

A: The solution is as follows:

Q: Find the equation of the tangent line to the curve y = x* + 6e* at the point (0, 6). y =

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Q: Find an equation for the tangent line to the curve y = 2/x at the point (2, 1) on this curve.

A: Given, Equation of curve : y=2x      (i) Common point = (2,1)

Q: x =t - sint y = 1- cost

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Q: The slope of the tangent line to the curve 2xy + T cos y = 2n at point (1,“) is:

A: The given equation is 2xy+π cos y=2π and the point is 1, π2. Evaluate the slope  y' using implicit…

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.