Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at which it occurs, namely find the maximum diree- tional derivative at (1,-1) and its direction.

Q: Determine the equation of the tangent line for y = sech(In x) + tan-(x²) tangent at x = e*. A. Yr =…

A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

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 derivative of y with respect to the appropriate variable. 1. y = cos-1 (x2)   2. y =…

A: Part 1. Given,

Q: Section 2.4 Chain Rule Please show & explain all work, thank you.

A: Multiply both sides by x^2.

Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

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Q: (x-y) atfy (1, 1) a+y

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Q: 3. Solve the first derivative of f(x) = evx at x = 0.5 using centered finite-divided difference and…

A: To find the first derivative of f(x) at x=0.5 using centered finite-divided difference and a step…

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: Where on the interval [0, 4] does ƒ(x) = 4x - x2 have a horizontal tangent line?

A: Determine the value for derivative of f(x) i.e f'(x). fx=4x−x2f'x=ddx4x−x2=ddx4x−ddxx2=4×ddxx−2xSo,…

Q: Compute the first derivative of y = 2x^4 - 6x^3 - 12x - 8 at the point x=0 based on the value at xo…

A: Five point FD Approximation and CD Approximation:--- ..  I this Error is 0%

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

A: To determine the equation of tangent line to the given curve at point (1, 0).

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: find the first order derivative of y=sin 0.5√x/x at x=8, h=0.2 a. Forward difference B. Backward…

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Q: Find the slope of the tangent line to the curve 2 sin(z) + 5 cos(y) – 4 sin(z) cos(y) + z = 7m at…

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Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

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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: Estimate the slope of the tangent line to y=x^2 at the point (1,1). Verify your answer analytically.…

A: Since multiple questions are asked, we will solve the question that the graph attached is related…

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

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

A: Given: fx=e3x

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: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

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: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 2. Find the derivative of: (a) A(x) = [ 1n | In(sin(3t)) dt (b) A(x) = L, In(sin(3t)) dt

A: According to the Leibinitz rule :

Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

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

A: Given equation of curve is (x2+y2-y)2=x2+y2 Differentiate both sides with respect to x.…

Q: Find the equation of the tangent to y-cos 2x at the point 0. Oal y--2- Ob) y- 2x+ O) y--+1 O d)…

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Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

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: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: Find the derivative of y with respect to s. y= sec -1(9s5 + 5)

A: To find the derivative of  y=sec-1(9s⁵+5)

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

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Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: Find the slope of the tangent line to the curve 5 sin(x) + 5 cos(y) – 6 sin(x) cos(y) + x = 6T at…

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Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

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: 3. Find the equation of the tangent line to f(x) = 2x · sin (x) at the point (5, ).

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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).

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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…

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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