Differentiate.  y =t / (t- 1) 2

Q: Find an equation of the tangent line at the given point.…

A: Given, y2ex2-16-xy-1=2Point=4, 2

Q: Find the equation of the tangent line to the graph of y?- x+1=0, at the point (2,-1). %3D

A: Here we havw to find the equation of the tangent line to the graph y2-x+1=0 at the point (2, -1)

Q: 5. Find the slope of the tangent line to the curve y + 2yx3 - x-5y3 = 0 at (0, 5). %3D

A:

Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

A:

Q: Find the derivative. 4 7(+3t) dt 7(P+31)-] 4 dt

A:

Q: Find slope of the tangent line to the elipse x^2/36 + y^2/16=1 at the point (x,y) slope=

A: Given ellipse equation is x236+y216=1 find the slope of the tangent line at the point (x,y)

Q: Find an equation of the tangent line to the curve: 4x^2 - 24xe^y + y = 13 @ the point (-1/2, 0).

A:

Q: Find y" by implicit differentiation. 3x3 + 5y3 = 7 y" II

A: Given       3x3+5y3=7   1using implicit differentiation, w.r.t x1  ddx(3x3) +ddx(5y3)=ddx(7)…

Q: 3. (D - 3D? + 4)y = 40cos2x + 6

A:

Q: Find y" by implicit differentiation. бх2 + у2 %3D 3 y" =

A: Given that implicit function is 6x2+y2=3 To find: y''Solution:6x2+y2=3 Diffranciate w.r.t…

Q: Find the point(s) on the graph y = x3 where the line through the point (4, 0) is tangent to y.

A:

Q: Find the first four derivatives of y = 4sinx. %3D

A:

Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A:

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: compute the derivative

A:

Q: Find the derivatives of the functions in Exercis

A: We need to find the derivative of the function, y=5-2x-3+182x+14

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: use differentials to approximate the change in y if x changes from 25 to 25.3

A:

Q: Find an equation of the tangent line to the curve y = 9^x at the point (2,81)

A: Given the curve is y=9^x at the point (2,81).

Q: find an equation of the tangent line f(x)=x+(6/x)    points (x,y)= (-6,-7)

A:

Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: Find an equation of the tangent line to the curve y=8ln((x^3)-26) at the point (3,0).

A: To determine equation of tangent line at given point.

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

A:

Q: Find y" by implicit differentiation. 2 + 6y = 6 y"

A: Here is the solution

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: compute the derivative. y = z csc(9z + 1)

A: y=z csc9z+1

Q: compute the derivative

A:

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

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 line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: Find the slope of the tangent line to the curve `-3 x^2 + 3 xy + 4 y^3 = 8` at the point (4,2)`.…

A:

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

A:

Q: 2. Write the equation of the tangent line to the curve y = x3 – 6x at the point (2, –4).

A:

Q: the side of a sqaure is 10 cm. find the approximately, by using differential, the increase in the…

A: Given that side of a square a is 10cm and it is increased by 0.02cm.

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

A:

Q: Find the equation of normal to the curve y = 2x – 4x² +x- 6 at point (2,–4)

A: Given y=2x3-4x2+x-6 and point is P(2,-4)We need to find the slope i.e. y'dydx=ddx(2x3-4x2+x-6)We…

Q: Find the equation of the tangent line to y = 20-5æ+3 at x = 4. y =

A:

Q: find dydx

A: The given equation is:

Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

A:

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

A:

Q: Find the derivative of the function. y = 4sin(Tx) y' = %3D

A:

Q: Find y" by implicit differentiation. 3x + y =5 3r y

A:

Q: Find the normal to the curve y = 1 - x2 at the point (3, -8).

A:

Q: ential equation is given by

A:

Q: Determine the equation of the line tangent to y = /1+x³ at the point (2, 3).

A: The given function is y=1+x3. Its derivative is obtained as, dydx=ddx1+x3=121+x3ddx1+x3=3x221+x3 at…

Q: Find the equation of the tangent line to the curve y = (1 + 2x)² at the point (4, 81). ソ=

A: First find the slope of the tangent line with the help of derivative of the given curve than write…

Q: Find the derivative of the function. 7. y%3D Vx +2 y'

A:

Q: Locate the point where the slope of tangent line to y-n 2r2 s

A:

Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: