I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z=-2 1+x? ; d²z/dx? 2. Y = (3x3 + 2)ª ;y" 3. Y= (2x + 1)2 yiv II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT. at ( 1, 2 ) 5. X2y3 - 2xy = 6x + y + 1 6. Y = (3 at x= 3 4. XY3 = 8 at ( 0, - 1) III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 7. Y = 3x$ – 5x³ + 4 8. Y = (2x – 1)² (x² - 9)

Q: Find equations of the tangent line and normal line to the curve at the given point. yy = √xx xx+1 at…

A: According to the given information, it is required to determine the equation of tangent and normal…

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

A:

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: Find the equation of the tangent line at the given value of x on the curve. 2y (x- 3) + xvy = 3; x=3…

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Q: 1. Find the equation of the tangent line to x2- 3xy +y2 = -1 at (2,1).

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

Q: 30. Determine the equation of the tangent to y= 2+ cos 2x at x

A:

Q: Find an equation of the tangent line to the curve atthe given point.   y =  Sin (2 In x) , (1 ,0)

A: Given curve,  y = sin(2 ln(x))  We have to find the tangent line to the curve at the point (1, 0)

Q: Find the equation of tangent and normal to the curve x sin 2y = y cos 2x at 4 2

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Q: Find the equation of the tangent line to the curve at the given point using implicit…

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Q: 6. Find the equation of the tangent line to x² + 3xy + y² = 5 at the point (1, –4).

A: Given x2+3xy+y2=5       (1,-4)

Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: 3. What is the slope of the tangent line to y = 4* at x = 0?

A:

Q: 4. Find the equation of the tangent line to the curve y = 5x– 6/x at the point (1, –1).

A:

Q: 2. Find the equation of the tangent line to the curve y = In(x'-7) at (2,0).

A: Given :          y=lnx3-7

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

A:

Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve z2+2ry-y²+x = 2…

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Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

A:

Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

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Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

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

A: Find dy/dx

Q: Determine the derivative of the function defined by h(x,y) = Arctan (2) + V3Arcsin () at the point…

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

A:

Q: Find the equation of the tangent line to the curve y = ex/x + ex at (0, 1).

A: Given that curve  y = exx+ex at (0, 1). The slope of tangent any point on the curve is given by its…

Q: 3) Find the equation of the tangent line to the curve 6y³ – xy² + cos (xy) = 7 - at the point (…

A:

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: 3. Find the equation of the tangent line to the curve x'y+y°x= 30 at point (1,3).

A: Solve the given problem.

Q: Find equations of the tangent and normal line to the curve y = x cos x at x = t/2.

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

A:

Q: 1) Find the equation of the tangent line to the curve: x* + xy – y = 7 at (3,2) %3D

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Q: Find the equation of the tangent line and normal line to the curve: 2. x2 + 2xy = y3 at the point…

A: Firstly, we find  dy/dx by differentiating both sides with respect to x

Q: Find an equation of the tangent line to ln(2x-y+1) + cos(xy-2)=1 at the point (1,2)

A: Given:

Q: y = xv16 + x², (0,0)

A: Topic:- application of derivatives

Q: Determine the slope of the tangent line to the curve y= In x^2 at x = e^2

A: The given curve is

Q: 4. Find the equation of the tangent line to the curve 2xy+r sin y = 27 at the point (1.%).

A:

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: Find the slope of the equation of the tangent line to the curve at (0,1). 2x y = e2* cos IX

A:

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: 2) Find the equation of the tangent line in slope intercept form to the curve x² + 4xy + y2 = 13 at…

A:

Q: 2/ Find the equation of the tangent line at (0,0) to fex) = xex хе 2 -X

A: Given f(x)=xe-x2y=xe-x2Differentiate…

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

A:

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the equation of the tangent line to the curve y= x4 + 6ex at the point (0,6). Enter exact…

A:

Q: Find the equation of the tangent line at the given value of x on the curve. 2y° + xy - y = 16x*; x=1…

A:

Q: 2 Find the equation of the tangent to the curve y = sin x at the point where x = . 3

A:

Q: 6. Find the equation of the tangent line to the curve 2x3 + xy + y° = 4 at the point (1, 1).

A: Firstly we can find slope .i.e, dydx at (1,1). Then slope intercept form  y-y1=m(x-x1)

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…