Sketch the graph of a differentiable function y = ƒ(x) through thepoint (1, 1) if ƒ'(1) = 0 and ƒ'(x) < 0 for x < 1 and ƒ'(x) > 0 for x> 1;

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: A function has a tangential gradient of 2sin3x. If the curve cuts the x-axis at, determine the…

A: A function has a tangential gradient  of 2 sin 3x.If the curve cuts the  x-axis at π3.To determine…

Q: Find the derivative of the function. 1 + x 1 - x y = arctan y' =

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Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: 1-x Find the derivative of y = arctan %3D 1+x

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Q: Find the derivative of the function f(x,y) = x +xy + y at the point (- 2,- 1) in the direction in…

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Q: Find the derivative of the function f(x.y) = tan -1y at the point (- 9,9) in the direction in which…

A: To find the derivative of a function at a point (-9, 9) in the direction in which the function…

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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Q: Use centered difference approximations to estimate the first and second derivatives of y = ex at x =…

A: The central difference for first and second derivative is calculated respectively,

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

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

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Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: What is the equation of the tangent line to the function y = e-* - arcsin) x+1 2. at x= 0 ? A) y-…

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Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: Find the derivative of the function y= arctan x +x/1+x2

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Q: Determine the derivative of y with respect to x: In x+ In y = x cos y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

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: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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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: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: Find the rate of change of y with respect to x at the indicated value of x. sin(x) y = 5 - cos(x) X…

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Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x &gt; 0

A: Given that, y=csc-1x2+1

Q: Find the derivative of the function. y = arctan 1 + x 1 - X y' =

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Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

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Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

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Q: What

A: The correct option is (B).

Q: Find all second order partial derivative with respect to variable x and y. F(х,у)- х сosxу + y sinx…

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Q: Determine the indicated (in the attached image) partial derivative of  f(x, y) = 3x3y2 + ln(2x2 -…

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Q: Use high-accuracy centered difference approximation to estimate the first and second derivatives of…

A: The central difference approximation to the first derivative of a function at is given by the…

Q: Find the derivative of the function. f(x) = In(sinh(x)) %3D f '(x) = %3D

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Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: Find the Partial derivative of f with respect to y for * f (x, y) = x+y

A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2

Q: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

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Q: Use the Second Derivative Test to determine the relative extremum trema) and saddle point(s), if…

A: This is a problem related to maxima and minima of the function. By first derivative test we will…

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Q: Find the gradient of the tangent line to the curve x² + y =10 at x=1, where y > 0. %3D

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