Find an equation for the line tangent to the graph of f(x)=−2xe^x at the point (a,f(a)) for a=2. y=

Q: h(x)=(x° +1} (2x+5)*

A: Given : hx = x2+132x+52

Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

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Q: 14. If x2 + y2 13, find at (2, 3). dx2 %3D

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Q: Find the derivative of x/ex^2.

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Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Find the equation of tangent line at the specified point  x power 2 by 3 - y power 2 by 3 - y =1…

A: Given curve is x23-y23-y=1. To find the equation of tangent line at the point 1,-1. Solution:…

Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

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Q: What is the slope of the tangent line to the curve y = 2sin 4x at x = 4

A: Given, The curve  y = 2sin4x   We have to find the slope of the tangent line to the curve at x = π4.…

Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: 8. Find the derivative of y = x arctan 2.x --In(1+4x). -- - 4.

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Q: Find the slope of the tangent line drawn to the graph of −4x^2−xy+3y^3=−200 at the point (−1,−4).…

A: Given function is : -4x2-xy+3y3=-200 To find out slope of tangent dydx at -1,-4 Differentiating…

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: Find the derivative of the function f(x.y) = tan -1 y at the point (4, - 4) in the direction in…

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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: The slope of the tangent line to the curve y 4 at the point (4, 1) is: - The equation of this…

A: The slope of tangent to any curve is determined by the derivative . So, slope of the tangent…

Q: Find the slope of the tangent line drawn to the graph of 2x2−xy−y3=5 at the point (2,1). Enter exact…

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Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: Find the equation of tangent line at the specified point  x ²/³ - y ²/³- y =1 ;(1, -1)

A: Given curve is x23-y23-y=1. To find the equation of tangent line at the point 1,-1. Solution: First…

Q: Find the slope of the tangent line to the curve 4x + lay- ly = 88 at the point (3, - 4).

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Q: Find the slope of the curve y = tan-!x at a1, b without calcu- 4 lating the derivative of tan-x.

A: Given y=tan-1x

Q: Find the derivative of fcx) = en (sinh Cx)) 5

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Q: The slope of the tangent to y = 2 – x2 at the point (1,1) is

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Q: Find the derivative of y given that y= x In x et

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Q: Find the equation of the tangent line to the curve y = xV13 – x² at the point (2,6).

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Q: What is the equation of the tangent line to the function y=x²-1 at a point (2,3)?

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Q: The slope of the tangent line to the curve y = 3 3 at the point (5,2) is: X -

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Q: Find an equation of the line tangent to the curve at the point (4, 0.4). 2Vx ソミ x+6 Equation:

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Q: 4 at the point ( 3, The slope of the tangent line to the curve y is:

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Q: Find the equation of the line that is tangent to y = 2log3(x + 1) and is perpendicular to the line y…

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Q: Calculate the derivative at the point (0,0) of the function given by the equation x=y−2siny.

A: We differentiate both sides with respect to x

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

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Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: i.) Find the tquation of the tangent line to the curve y= 2+4x- x° at the point P(-1,-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 line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: So far, you've examined the function y = In x and its derivative, y' = , for large values of x. Now,…

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Q: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: What is the derivative of: 4 ln(sec y + tan y) − 2x − sin 2x = 1

A: Given: 4 lnsec y+tan y-2x-sin 2x=1 To Find: dydx=?

Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: What is the equation of the tangent line of y=4(x^3)-7(x^2) at the point x=3

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Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: