28. Use mplicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy +4y? = 12, (2,1) 50-52 Find the derivative of the function. 50. y = tan-1(x²) 52. g(x) = arccos (Vx)

Q: 2. Use Desmos to graph the function y3 + yx² + x² – 3y² = 0 and estimate the slope of the tangent…

A: Given,          The function is y3+yx2+x2-3y2=0.

Q: Find an equation of the tangent line to the graph of the function at the given point

A: To find the slope we find y' at x=0, y=0

Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

A: The equation of tangent line can be found by using the formula,y-y1=mx-x1Where, m=dydxx1

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: 5. Find the equation of the tangent line to the curve of the function Y= 2x-x +2 at the point (1,3).

A: Given,  y = 2x3-x2+2   and the point 1, 3 We have to find the equation of the tangent line at the…

Q: 1. Find the equation of the tangent and normal line to the curve f(x) =x' - 3x +2 at (1, 0).

A: Given the function f(x) :

Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: 3. Find the equation of the tangent line to the curve x2 – 2x In y + 3y2 = 3e2 - 1 in the point (1,…

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Q: 2. Find the equation of the tangent and normal line of the function y+ 3xy +x = 5 at the point (1,…

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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: 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. Find the equation of the tangent line to the curve y = x³ at x=1.

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

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

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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).

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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: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

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

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Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

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Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

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Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Can you help me with this problem step by step?

A: The given equation,

Q: 2. Use implicit differentiation to find the tangent line to the given curve at the given point P (a)…

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Q: 4. Find the equation of the tangent line to g(x) 8 at x = 3 |x²–1

A: The function is given by gx = 8x2-13 To evaluate: The equation of the tangent line to the graph of…

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

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Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: Find the equation of tangent line for the curve f(x)=e³x at coordinate (0,1).

A: Given: fx=e3x

Q: find the derivative of y with respect to the appropriate variable.13. y = 6 sinh x/3 14. y = 1/2…

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Q: 3. Find an equation of the tangent line to the curve at x=4 y=(sqrt(x)) / (x+6)

A: Given equation of the curve y = xx+6  ...............(1) Let the equation of the tangent at (x1, y1)…

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: 1) Find the derivative of y with reference to < Y 블+름 2y Y

A: Here is the solution:

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

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

A: Follow the procedure given below.

Q: 6. Find an equation of the tangent line to y = f(x) : = tan¬(2x) at x = 7

A: Given,

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: 2. Find the equation of the tangent line to y at x = -5.

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Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: curve at the following point:  y = 2/ 1 + e-x, (0,1)

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Q: Find the derivative of y with respect to x for y = sinh - 1 ' (11/9x).

A: From the given problem:   y=sinh-1119x...(1)   Now simply write as: 119x=11· 3x=33x   Substitute…

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

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

A: given that x2-3xy+y2=-1slope of tangent (m)= dydxdifferntiate the given curve with respect to…

Q: 6. Find the equation of the tangent line to the curve y = e when it is parallel to 2x- y=7.

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Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

A: We have to find derivative of y with respect to the appropriate variable: y=12 sinh 2x+1 We know…

Q: 8) Using your derivative from the previous question, determine the equation of the tangent line at…

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

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Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

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: If 2x2 + 5x + xy = 4 and y(4) = -12, find y (4) by implicit differentiation. y (4) = Thus, an…

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