3) Given the function g(x)= 2x² – 5x a) Find the derivative using the limit definition. b) Find the slope of the line tangent to this curve at x=1. c) Find the instantaneous rate of change of the function when x=1.

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

A: Multiply both sides by x^2.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use the definition of a derivative to find the equation of the tangent line at the given point.…

A: The equation of the tangent line is  y-7x+2=0

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

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Q: By the chain rule, the derivative of arctan (4x^5) is:

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Q: Find the derivative of the follourng funchion y=x sin'x %3D

A: We have to find the derivative of the given function   The given function is y=x sin-1x3it can…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x? +…

A: We need to find instantaneous rate of change of  f(x)=2x2+5x+7 at x=3, using limit definition of the…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 6x +…

A: Formula use Instataneous rate of change og f w.r.t x at a i f'(a) = lim f(a+n)-f(a) / n…

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 slope of the tangent line to the curve defined by 4x + xy – y* 1760 at the point (8, –4). e…

A: To find the slope of the tangent line to the given curve at the given point

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: 3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in…

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Q: 3. Use the limit definition of the derivative to find the equation of the tangent line to the curve…

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(z) = 7x² +…

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Q: 2) NOT use the short cut method). Use the result to find the slope of the tangent line at the point…

A: Topic:- Derivative

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Find the derivative of the function using the slope limit formula. 1 y= 3-х 1. y=(3x+1)2 2. 1 y= 1…

A: Note : As per our company guide lines, we are supposed to answer only one question. Kindly post…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: Recall: Slope of the tangent line using the definition of  limit of the derivative:…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: If fx)=- has a tangent equation y/3-x+2 at x = 1, then the slope of the tangent line of f ( x) at…

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 3x + 5x…

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Q: Find the derivative of the function (slope of the tangent) using the definition at the point Xo=9…

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x² +…

A: We will find the instantaneous rate of change of f(x) at x=4 as following.

Q: Find the derivative at the given x-value with the appropriate rule. y=4-18sqrt x at x=4

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x +…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use the definition to find the derivative of the function f(x) = Vx +1 and obtain the equation of…

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Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: Use the definition of derivative to find the slope of the tangent line to the function f(x) = V2x at…

A: Let's find.

Q: Use the limit definition of the derivative to find the instantaneous rate of change of…

A: The limit definition of derivative is as shown below:

Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

A:

Q: Calculate the derivative of f1 (x) = √1−2x by using the definition of the derivative as the limit of…

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Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Let f(x) : 3x Using the limit definition of the derivative, find the equation x +1 of the line…

A: Given data: The given function is f(x)=3x/(x+1). The given point is (a, b)=(2, 2). The expression…

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve…

A: Question is solved.

Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve…

A:

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

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: