Let f(x) 2.x2. Then f'(x) = 4.x. Find the equation of the tangent li at x = 1 for f (x). That is, find the equation of the linear function that has slope f'( which passes through the point (1, f(1)).

Q: 2. Find the slope of the tangent line to the curve y = x3 – 2x + 1 at x = 1.

A: As we know that: The first derivative of the function at a point is equal to the slope of the…

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given…

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: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

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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: Find the equation of the tangent line at the given value of x on the curve. y° +xy² -61=x+3y°; x:…

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Q: Find the slope of the tangent to the curve y x3 at (6, 3) xy + 6 dx (Enter undef if the slope is not…

A: Given that: y2=x3xy+6 at (6, 3)

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: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

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 the equation of the tangent plane to the graph of g(x, y) = ln(6x² – 3y²) at the point (1, 1).…

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Q: 5. Find the equation of the tangent line on x² + y? = (2x² + 2y² – x)² at (0, ).

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Q: Find the derivative of y with respect to x. y = (x° In x) ³ dy dx II

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Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: Find the slope of the tangent line of the function -ey + x2 – y = 15 at the point (4,0)

A: Please note that the slope of tangent to a curve at any point is given by the derivative of the…

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: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3.

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Q: Find the derivative of y with respect to x. y = (6x + 5)* dy dx II

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Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y =…

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Q: Find the point of intersection of the tangent line to y=sin 2x) at y=0 and the line x+2y=5-

A: Given: y=sin(2x)  and y=0       substituting y=0 in y=sin(2x)then    0=sin(2x)         2x=0…

Q: Find the slope of the tangent line to the curve y3 + yx2 + x2 − 3y2 = 0 at the point P(0, 3) by…

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Q: Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

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Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

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

A: Given: fx=e3x

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

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Q: *4. Find the equation of the tangent line to r² – 3ry + y² = -1 at (2,1).

A: Equation of tangent at a point

Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: Find the equation of the tangent line at the given value of x on the curve. y+xy² -22=Dx+5y; x= 5

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Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

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: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: f(x) = ln(x − 1) at x = 2

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 equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

A: Given:

Q: Find the derivative of y with respect to x. 6 y = (x³ In x) %3D dy dx II

A: Please see the below picture for detailed solution.

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: Find the derivative of y with respect to x. 1 y = In x/x+5 dy dx II

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Q: The slope of the tangent line to the graph of xy = In(x² + y²) at the point (1, 0) is

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: The gradient of the tangent to the curve = 4x + y at the point (0, 1) is D - 2

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Q: Find the derivative of y with respect to x if y = (10x- 20x + 20) ex. %3D dy dx

A: We can make it easier for you

Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

A: