Use the graph of y = f(x) in the accompanying figure to estimate the value of f'(1), f'(3), f'(5), and f'(6).

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Compute the derivative of the function y=arcsin1√x at x=2.

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Q: What is the second derivative of f(x)=6x^4 at the point x=−2?

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Q: Find the derivative. y= In x+3 %3D

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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: f(x)= xe* In(x³)

A: f(x)=xe-xln(x3)According to question we have to calculate the derivative of the function.

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

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Q: Find the derivative of the function using 3-step rule: v (t) = -.

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Q: Determine the derivative of the function y=arcsin 2x / 1+x2 at x=2.

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Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Find the derivative of f(x)=arctan(1/x) and simplify

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Q: Find the derivative of 3 In xy + sin y = x².

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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: What is the derivative of * y = arctan(x2 + 1)?

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Q: Determine the derivative of y=(x−1)4 without using the power rule.

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: Find the derivative of f(x)= xtan(x)

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Q: find the equation of the tangent line to the graph of f(x) = x^3 + 3x^2 at the point (1, 4) without…

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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 the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: Find the derivative. y = ecosh(8x) y'(x) =

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Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: The second derivative of the function is y = arctan 2x

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Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: find the derivative of the funciton y=xe^(5x)

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Q: Find the derivative of the function. y = In(Icsc(7x)|) y'(x) =

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Q: Find the derivative of the functiony=tan^2(6x)

A: we have to find derivative of f(x)we will use following rules

Q: Find the derivative of the function defined by the equation x+y=arctan(xy).

A: To find the derivative of the given function.

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

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

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Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of: x²y = (y + 2) + ry sin(x)

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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: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: Find the derivative of the function f(x y) = tan-1Y at the point (5, -5) in the direction in which…

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Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: 1. y= ArctanB %3D 3-V9-x2

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Q: 4) Find the derivative of y = arctan(x² + 3)

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Q: Draw the function x = 2y-y2 by using the tools of derivatives?

A: The given function isx=2y-y2.

Q: 9 y = Arctan(+x, 1- 2x

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Q: Compute the derivative of f(x) = arcsin(x² e3=).

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Q: What is the derivative of y = etan-1 2x 2

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Q: Find the derivative using the definition 1- y = vx -1

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Q: 2.) y = tan¬1 – 6•x³ y' =

A: We have to find the derivative of the function: y=tan-1-6·x3 We know the formula of derivatives,…

Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

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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.

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